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Busc2112-basic-calculus-week-5-7-7101216 compress
Calculus-Based Physics 1 (AMA Computer University)
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = ( x2 )
Answer:
2
-1
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=x
Answer:
1
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1, b = 2, and c = 3.
f (x) =
Answer:
7x
3
−
3b
c
2.33
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = (5)(4x2 − 7)(6x2 − 1)
Answer:
2920
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
x
f (x) = 2xe
Answer:
0
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
−−
y = √−
x + 5√5x
Answer:
2.14
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1. Use 3.14 for the value of pi.
–
y = √2x + 3π − 12
Answer:
0.4
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−−−−−−
y = √−
4x2 − 6x + 1 −
Answer:
3
−−−
−
4√x+1
0.1434
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = (3x)(4x2 − 5x + 1)3
Answer:
0
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 24(x3 + 6x)
Answer:
3
8
24.00
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
3
4
Answer:
5 −
−
√x2 −
6
−
√x
−
+x
1
3
2.96
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
1
h(x) = 4x2 e x
Answer:
10.87
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
1
y = 3x 4 −
Answer:
1
3x
6 −
−
+ 14√x5
12.75
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
f (x) = ln(e x + e
2
Answer:
x)
−2
0
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
G(x) = √−5−−x
2
Answer:
3134
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1 and s = 2. Use 3.14 for the value
of pi.
f (x) = 5s + 3π − 12
Answer:
0
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
h(x) = (log x )(3 x )
2
Answer:
2
2
3
2285525343
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y=
4
(5)(6x−5)
Answer:
10
-2.43
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = (3x − 7)(x2 + 4x − 5)
Answer:
-24
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
x2 −6x
−−−
−
√x−3
Answer:
0.14344
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = (6x − 5)√−
8x − 3
Answer:
15.21
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = 2 − √−
4 − 5x
3
Answer:
1.6
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 5x
Answer:
1
5
−
x−
2
7
5 −
−
+ √x4
2.09
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
–
y = 3√5x + 6x2 − 23 x3 + 8
Answer:
16.71
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
−
g(x) = e√1−2x
Answer:
1
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 5x−5 + 37 x−14 − 12x3
Answer:
-67
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
x
y = (2x + 1)
Answer:
5.30
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
3x+5
(2x−3)
Answer:
3
-51
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
x
f (x) = 2xe
Answer:
0
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 73x
2
Answer:
−4x+5
9344.26
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
−
y = √−
x + 5√−
5x
Answer:
2.14
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=x
Answer:
1
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = ( x2 )2
Answer:
-1
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
x)
y = ( 2x4−3 )( 12−
2
Answer:
2.375
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
6
−−
7∗√x4
7
Answer:
−
5x6
12
− 24
-2.99
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = 2 − √−
4 − 5x
3
Answer:
1.6
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
x2 +5
2x−3
Answer:
-14
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = (2x + 1)x
Answer:
5.30
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y=
e√2x+1
−−−−
−
√2x+1
Answer:
0.21
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1 and a = 2.
f (x) =
Answer:
x2
4
+
x
5
−
a
3
+7
0.7
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = (5x − 6)4 (2x + 3)5
Answer:
-56250
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
−−−−−−−−−
y = √−
3x2 + 5x − 8
Answer:
2.27
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1. Use 3.14 for the value of pi.
y = √–2x + 3π − 12
Answer:
0.4
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y= x
+
Answer:
-20.02
5
4
x
−
√
8
−
x
3−
√
4
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y=
x
x
2
+5
2 −3
Answer:
-14
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = (5)(4x
2
Answer:
x
− 7)(6
2
− 1)
2920
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
G(x) = √−5−−x
2
Answer:
3134
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y=
2x−1
x2 +2x+1
Answer:
0
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
3
4
Answer:
5 −
−
√x2 −
6
−
√x
+
x−
1
3
2.96
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
3x+5
(2x−3)
Answer:
3
-51
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 24(x3 + 6x)
Answer:
3
8
24.00
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 34 x4 − 3x5 −
Answer:
2x6
3
-16
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 3x
Answer:
1
4
−
1
3x
6 −
−
+ 14√x5
12.75
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
√
3
Answer:
−−
−−−−
3x+4 2
( 4x−3 )
-8.71
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 4x
Answer:
4
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = (6x − 5)√−
8x − 3
Answer:
15.21
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
x2 −6x
−−−
−
√x−3
Answer:
0.14344
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
−−
−−−−−−
2
−3x+1
g(x) = 3√x
Answer:
3
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−−−−−−−
3
y = √4x2 − 6x + 1 − 4√−
−−
−
x+1
Answer:
0.14344
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1. Use 3.14 for the value of pi.
y = x3 + 5x2 − 4π
Answer:
13
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y=
4
(5)(6x−5)
Answer:
10
-2.43
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 3x
Answer:
1
−
4
1
3x
6 −
−
+ 14√x5
12.75
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
6
5x3
Answer:
−
5x
4
−
1
3x3
-3.85
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 4x
Answer:
4
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
f (x) = (23x
4
Answer:
)(5
x2
)
461.47
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = ( x2 )2
Answer:
-1
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = x6 +
Answer:
1
2x
4 −
−
+ 8√x3
11.50
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = (6x − 5)√−
8x − 3
Answer:
15.21
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
f (x) = ln(e2x + e−2x )
Answer:
2.00
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
x2 −6x
−−−
−
√x−3
Answer:
0.14344
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = (3x − 7)(x2 + 4x − 5)
Answer:
-24
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
√
3
Answer:
−−
−−−−
3x+4 2
( 4x−3 )
-8.71
Question 3
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 73x −4x+5
2
Answer:
9344.26
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Performance Task 1
Question 4
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 3√–5x + 6x2 − 23 x3 + 8
Answer:
16.71
Question 5
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
6
y = 34 x4 − 3x5 − 2x3
Answer:
-16
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = √−
4−−−−−−−−
1 − 4√−x3−+1
x2 − 6x + −
−−
Answer:
0.14344
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = x54
Answer:
−
3−
+ √8x − √4x
-20.02
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Performance Task 1
Question 8
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
−−−−
y = 2 − √−
4 − 5x
3
Answer:
1.6
Question 9
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1, b = 2, and c = 3.
f (x) =
Answer:
7x
3
−
3b
c
2.33
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
1
2
Answer:
0
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 34 x4 − 3x5 −
Answer:
2x6
3
-16
Question 2
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
y = ( x2 )2
Answer:
-1
Question 3
Answer saved
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Compute for the derivative of the function below for x = 1 and a = 2.
f (x) = 2a
Answer:
0
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Question 4
Answer saved
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Compute for the derivative of the function below for x = 2.
f (x) = ln(e2x + e−2x )
Answer:
2.00
Question 5
Answer saved
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Compute for the derivative of the function below for x = 1 and s = 2. Use 3.14 for the value
of pi.
f (x) = 5s + 3π − 12
Answer:
0
Question 6
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
5
x4
Answer:
+
−
√x
8
−
3−
√x
4
-20.02
Question 7
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 2.
4
y=
(5)(6x−5)
Answer:
10
-2.43
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Question 8
Answer saved
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Compute for the derivative of the function below for x = 1.
x
f (x) = 2xe
Answer:
0
Question 9
Answer saved
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Compute for the derivative of the function below for x = 1.
1
y = 3x 4 −
Answer:
1
3x
6 −
−
+ 14√x5
12.75
Question 10
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y = 12
Answer:
0
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
Marked out of 1.00
Compute for the derivative of the function below for x = 1.
y=
3
4
Answer:
5 −
−
√x2 −
6
−
√x
+
x−
1
3
2.96
Question 2
Answer saved
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Compute for the derivative of the function below for x = 1.
y=
3x+5
(2x−3)
Answer:
3
-51
Question 3
Answer saved
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Compute for the derivative of the function below for x = 1.
−−−−
y = (6x − 5)√−
8x − 3
Answer:
15.21
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Question 4
Answer saved
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Compute for the derivative of the function below for x = 2.
−−−−−−−−−
y = √−
3x2 + 5x − 8
Answer:
2.27
Question 5
Answer saved
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Compute for the derivative of the function below for x = 2.
x
y = ( 2x4−3 )( 12−
)
2
Answer:
2.38
Question 6
Answer saved
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Compute for the derivative of the function below for x = 2.
−
y = √−
x + 5√−
5x
Answer:
4.31
Question 7
Answer saved
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Compute for the derivative of the function below for x = 2.
y=
x2 +5
2x−3
Answer:
-14
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Question 8
Answer saved
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Compute for the derivative of the function below for x = 1.
y = (5x − 6)4 (2x + 3)5
Answer:
-56250
Question 9
Answer saved
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Compute for the derivative of the function below for x = 2.
g(x) = 3
Answer:
−−−−−−−−
√x2 −3x+1
9.89
Question 10
Answer saved
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Compute for the derivative of the function below for x = 1.
y = (3x − 7)(x2 + 4x − 5)
Answer:
-24
◄ Some Tips in Computing Derivatives
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Week 008 - Higher Order Derivatives ►
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Performance Task 1
Home / My courses / BAED-BUSC2112-2022S / Week 7: Derivatives of Algebraic and Exponential Functions / Performance Task 1
Question 1
Answer saved
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Compute for the derivative of the function below for x = 1.
1
h(x) = 4x2 e x
Answer:
10.87
Question 2
Answer saved
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Compute for the derivative of the function below for x = 1.
f (x) = (23x )(5x )
4
Answer:
2
461.47
Question 3
Answer saved
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Compute for the derivative of the function below for x = 1.
y=
x2 −6x
−−−
−
√x−3
Answer:
0.14344
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Question 4
Answer saved
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Compute for the derivative of the function below for x = 1.
y = 3√–5x + 6x2 − 23 x3 + 8
Answer:
16.71
Question 5
Answer saved
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Compute for the derivative of the function below for x = 1.
y = (2x + 1)x
Answer:
5.30
Question 6
Answer saved
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Compute for the derivative of the function below for x = 1.
y = 6x − 12(4x2 − 3)2
Answer:
-186
Question 7
Answer saved
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Compute for the derivative of the function below for x = 1. Use 3.14 for the value of pi.
y = x3 + 5x2 − 4π
Answer:
13
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Question 8
Answer saved
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Compute for the derivative of the function below for x = 1.
y=
x2 +5
2x−3
Answer:
-8
Question 9
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Compute for the derivative of the function below for x = 1.
y = 24(x3 + 6x)
Answer:
3
8
24.00
Question 10
Answer saved
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Compute for the derivative of the function below for x = 2.
y = (5)(4x2 − 7)(6x2 − 1)
Answer:
2920
◄ Some Tips in Computing Derivatives
Jump to...
Week 008 - Higher Order Derivatives ►
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x3 + 3; at(−1, 4)
Answer:
0.14344
Question 2
Answer saved
Marked out of 1.00
Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
6
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Question 3
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Is the given function continuous at x = 3?
Select one:
a. Yes, since the piecewise function is defined at x = 3.
b. Yes, since the graphs of the sub-functions will meet at x = 3.
c. No, since the piecewise function is undefined at x = 3.
d. No, since the graphs of the sub-functions will not meet at x = 3.
Clear my choice
Question 4
Answer saved
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Evaluate the limit of:
limy→−3 log2 3y 2
Answer:
4.75
Question 5
Answer saved
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Evaluate the limit of:
limx→4 xx2 −64
−16
3
Answer:
6
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Question 6
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x2 ; at(2, 4)
Answer:
-4
Question 7
Answer saved
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Evaluate the limit of:
limx→1
Answer:
x−1
−
−−
−
√x+3 −2
0
Question 8
Answer saved
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Evaluate the limit of:
limx→0
sin3x
x
The given angle is in radians.
Answer:
3
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Long Quiz 001
Question 9
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Evaluate the limit of:
limx→2 log5 (4x3 + 5)
Answer:
2.24358
Question 10
Answer saved
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Evaluate the limit of:
limx→2
Answer:
–
−
√x−√2
x−2
0.14344
Question 11
Answer saved
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Evaluate the limit of:
limx→2
Answer:
x2 +2x−8
5x−10
1.2
Question 12
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Evaluate the limit of:
limx→3 log2 3x
Answer:
3.17
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Question 13
Answer saved
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Evaluate the limit of:
limx→0
Answer:
−
−−
−
√1+x−1
x
0
Question 14
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Evaluate the limit of:
limx→0
cos x
sin x−3
The given angle is in radians.
Answer:
-0.3
Question 15
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Evaluate the limit of:
limx→3 (x2 + 7x − 5)
Answer:
25
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Long Quiz 001
Question 16
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Is the given function continuous for all real numbers?
−
2 −−
f (x) = √−
x−
+1
Select one:
a. No, since the function's graph can only be generated using a table of values.
b. No, since the function will be undefined for some values of x.
c. Yes, since analytical methods can be used to graph the function.
d. Yes, since the function will always be defined for any value of x.
Clear my choice
Question 17
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
x2 − y 2
Answer:
= 7; at(4, −3)
2.3
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Question 18
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Is the given piecewise function continuous for the defined interval?
Select one:
a. No, since there are some values of x where the piecewise function is undefined.
b. No, since the graphs of the sub-functions will not meet within the interval.
c. Yes, since the graphs of the sub-functions will meet at a common point.
d. Yes, since the piecewise function will always be defined for any value of x.
Clear my choice
Question 19
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Evaluate the limit of:
limx→2 4x − 5
Answer:
3
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Question 20
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Is the given function continuous for all real numbers?
f (x) =
2
x2 −x
Select one:
a. Yes, since the function is always defined for any real number.
b. No, since the function cannot have some values in its domain.
c. Yes, since the function can be graphed using analytical methods.
d. No, since the function can only be graphed using a table of values.
Clear my choice
◄ Equation of a Tangent Line
Jump to...
Week 006 Calculus I - Differentiation Formulas ►
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Evaluate the limit of:
x
x
limx→2 (5 + 2 + 4)
Answer:
33
Question 2
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
6
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Question 3
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Is the given piecewise function continuous for the defined interval?
Select one:
a. Yes, since the graphs of the sub-functions will meet at x = 0.
b. No, since the graphs of the sub-functions do not have a common point.
c. Yes, since the piecewise function will always be defined within the interval.
d. No, since there are some values of x where the piecewise function will be undefined.
Clear my choice
Question 4
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A wholesaler who sells a product by the kilo (or fraction of a kilo) charges PhP 100 per kg if
10 kilos or less are ordered. If more than 10 kg are ordered, the wholesaler charges PhP
1,000 plus PhP 70 for each kg in excess of 10 kg. Is there continuity with the function
resulting from this selling strategy of the wholesaler?
Select one:
a. The resulting piecewise function is continuous since it will always be defined for any value of x.
b. The resulting piecewise function is continuous since the graphs of its sub-functions will meet at a specific value of x.
c. The resulting piecewise function is not continuous since the graphs of its sub-functions will not meet exactly at x = 10 kg.
d. The resulting piecewise function is not continuous since there are restrictions to its domain values.
Clear my choice
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Long Quiz 001
Question 5
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Is the given function continuous for all real numbers?
x+4
f (x) =
(x−1)(x+8)
Select one:
a. No, since the function will be undefined at both x = 1 and x = -8.
b. Yes, since the function can be graphed using analytical methods.
c. No, since the function will be undefined at x = 1 only.
d. Yes, since the function will always be defined for any value of x.
Clear my choice
Question 6
Answer saved
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Evaluate the limit of:
limx→0
Answer:
−
−−
−
√1+x−1
x
0
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Long Quiz 001
Question 7
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Is the given piecewise function continuous at x = 3?
Select one:
a. No, since the piecewise function will be undefined at x = 3.
b. No, since the graphs of the sub-functions do not have a common point.
c. Yes, since the piecewise function is defined at x = 3.
d. Yes, since the graphs of the sub-functions meet at x = 3.
Clear my choice
Question 8
Answer saved
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Evaluate the limit of:
3 −
−−−−
limx→5 log3 √x2 + 4
Answer:
1.02168
Question 9
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x2 + 4; at(−1, 5)
Answer:
1
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Long Quiz 001
Question 10
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
6
Question 11
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 1 − x3 ; at(2, −7)
Answer:
-12
Question 12
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x2 ; at(2, 4)
Answer:
1
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Question 13
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Evaluate the limit of:
limx→−2
Answer:
x3 −x2 −x+10
x2 +3x+2
-15
Question 14
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Is the given function continuous at x = 0?
−−−−
−
√x+16−4
f (x) =
x
Select one:
a. No, since the function has a value of 0.13 at x = 0.
b. Yes, since the function has a value of 0.13 at x = 0.
c. Yes, since the function is defined at x = 0.
d. No, since the function is undefined at x = 0.
Clear my choice
Question 15
Answer saved
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Evaluate the limit of:
limx→3
Answer:
x−3
−
−−
−
−
−−
−
√x−2 −√4−x
1
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Long Quiz 001
Question 16
Answer saved
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Evaluate the limit of:
limx→3 (
Answer:
−−
√3x
−
−−
−
x√x+1
)
0.5
Question 17
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Evaluate the limit of:
limx→0
sec x−1
x
The given angle is in radians.
Answer:
0
Question 18
Answer saved
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Evaluate the limit of:
−−
limx→3 (x2 √−
x−
+ 6)
Answer:
27
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Long Quiz 001
Question 19
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Is the given function continuous at x = 4?
f (x) =
1
x
−
1
4
x−4
Select one:
a. No, since the function is undefined at x = 4.
b. Yes, since the function is defined at x = 4.
c. Yes, since the value of the function at x = 4 is -0.06.
d. No, since the value of the function at x = 4 is -0.06.
Clear my choice
Question 20
Answer saved
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Is the given function continuous at x = 3?
Select one:
a. No, since the piecewise function is undefined at x = 3.
b. No, since the graphs of the sub-functions will not meet at x = 3.
c. Yes, since the piecewise function is defined at x = 3.
d. Yes, since the graphs of the sub-functions will meet at x = 3.
Clear my choice
◄ Equation of a Tangent Line
Jump to...
Week 006 Calculus I - Differentiation Formulas ►
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
Answer saved
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Is the given function continuous at x = 1?
f (x) = 2x2 − 3x + 1
Select one:
a. No, since the function is undefined at x = 1.
b. Yes, since the value of the function at x = 1 is 4.
c. Yes, since the function is defined at x = 1.
d. No, since the value of the function at x = 1 is 4.
Clear my choice
Question 2
Answer saved
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Is the given piecewise function continuous at x = 1?
Select one:
a. Yes, since the graphs of the sub-functions meet at x = 1.
b. Yes, since the piecewise function is defined at x = 1.
c. No, since the graphs of the sub-functions will not meet at x = 1.
d. No, since the piecewise function is undefined at x = 1.
Clear my choice
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Question 3
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 2 + x2 ; at(−1, 3)
Answer:
-2
Question 4
Answer saved
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Evaluate the limit of:
limx→2
Answer:
√
−
−−−
3−
x−
+2x+3
2
x +5
1.29
Question 5
Answer saved
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What is the slope of the tangent line at the given point?
y = x2 + 4; at(−1, 5)
Answer:
-2
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Question 6
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Evaluate the limit of:
lim →0
x
2
cot x
csc x
The given angle is in radians.
Answer:
1
Question 7
Answer saved
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Evaluate the limit of:
lim →1 √−−−+3−1−−2
x
x
x
Answer:
0
Question 8
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Evaluate the limit of:
−−−−−+4−
lim →4 √3 2 2−3
2 − −1
x
x
x
Answer:
x
x
0.67
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Question 9
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = 2 + x2 ; at(−1, 3)
Answer:
2
Question 10
Answer saved
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What is the slope of the tangent line at the given point?
y = 2 + x2 ; at(−1, 3)
Answer:
-2
Question 11
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 2x2 + 4x; at(−2, 0)
Answer:
-4
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Question 12
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Is the piecewise function below continuous at x = -3 or not?
Select one:
a. The piecewise function is continuous at x = -3 since it is defined for the said value of x.
b. The piecewise function is not continuous at x = -3 since the graphs of its sub-functions do not meet at this value of x.
c. The piecewise function is continuous at x = -3 since the graphs of its sub-functions meet at this value of x.
d. The piecewise function is not continuous at x = -3 since it is undefined for the said value of x.
Clear my choice
Question 13
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
-1
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Question 14
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Is the given function continuous at x = 5?
f (x) =
–
−
√x−√5
x−5
Select one:
a. No, since the value of the function at x = 5 is 0.22.
b. No, since the function is undefined at x = 5.
c. Yes, since the value of the function at x = 5 is 0.22.
d. Yes, since the function is defined at x = 5.
Clear my choice
Question 15
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Evaluate the limit of:
limx→−1 3
Answer:
−−−−−−−−
√x2 −3x+1
6.71
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Question 16
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Is the given piecewise function continuous for the defined interval?
Select one:
a. Yes, since the graphs of the sub-functions will meet at a common point.
b. Yes, since the piecewise function will always be defined for any value of x.
c. No, since the graphs of the sub-functions will not meet within the interval.
d. No, since there are some values of x where the piecewise function is undefined.
Clear my choice
Question 17
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What is the value of the derivative for the given value of t?
f (t) = (2t − 5)(3t + 4); whent =
Answer:
1
2
-1
Question 18
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What is the slope of the tangent line at the given point?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
-1
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Question 19
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Is the given function continuous for all real numbers?
f (x) = x3 − 6x2 − x + 30
Select one:
a. Yes, since the function will always be defined for any value of x.
b. Yes, since analytical methods can help generate the graph of the function.
c. No, since the graph of the function can only be generated using a table of values.
d. No, since there are some values of x where the function will be undefined.
Clear my choice
Question 20
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 42 − 4x + 1; atx = 1
Answer:
-4
◄ Equation of a Tangent Line
Jump to...
Week 006 Calculus I - Differentiation Formulas ►
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Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Is the given piecewise function continuous at x = 0?
Select one:
a. No, since the piecewise function is undefined at x = 0.
b. Yes, since the graphs of the sub-functions will meet at x = 0.
c. No, since the graphs of the sub-functions will not meet at x = 0.
d. Yes, since the piecewise function is defined at x = 0.
Clear my choice
Question 2
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
1
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Question 3
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Evaluate the limit of:
limx→0
sin 5x
2x
The given angle is in radians.
Answer:
2.5
Question 4
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x3 + 2x; atx = 0
Answer:
0
Question 5
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Evaluate the limit of:
−−−−−−−−
limx→−1 (x2 + 2)√x2 + x + 5
Answer:
6.71
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Question 6
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Evaluate the limit of:
limx→1 (x2 + 3x − 4)
Answer:
0
Question 7
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What is the value of the derivative for the given value of t?
f (t) = (t3 − 2t + 1)(2t2 + 3t); t = −3
Answer:
405
Question 8
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Evaluate the limit of:
limx→2
Answer:
√
−
−−−
3−
x−
+2x+3
x2 +5
1.29099
Question 9
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Evaluate the limit of:
3−
√x−1
limx→1 x−1
Answer:
0.3
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Question 10
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What is the value of the derivative for the given value of x?
y = x35 ; whenx = 1
Answer:
35
Question 11
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Evaluate the limit of:
limx→2 (
Answer:
x+3
)
x2 +x+5
0.45
Question 12
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Evaluate the limit of:
limx→√–2
Answer:
2x2 −3x+6
x2 +2
1.44
Question 13
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What is the value of the derivative for the given value of x?
y = x3 − 3x2 + 5x − 2; x = 7
Answer:
110
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Question 14
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Is the given function continuous at x = -3?
Select one:
a. Yes, since the graphs of the sub-functions will meet at x = -3.
b. Yes, since the piecewise function is defined at x = -3.
c. No, since the graphs of the sub-functions will not meet at x = -3.
d. No, since the piecewise function is undefined at x = -3.
Clear my choice
Question 15
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Evaluate the limit of:
limx→2
Answer:
x2 −6x+8
x3 −4
0
Question 16
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What is the slope of the tangent line at the given point?
y = 2x−2 ; at(1, 2)
Answer:
-4
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Question 17
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Evaluate the limit of:
−−−−−−−−−
limx→−2 √x2 + 2x + 8
Answer:
2.83
Question 18
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Is the given function continuous for x greater than -2?
f (x) = 2x3 + 5x2 − 7
Select one:
a. No, since the function can only be graphed using a table of values.
b. No, since the function will be undefined for some values of x.
c. Yes, since the function can be graphed using analytical methods.
d. Yes, since the function will always be defined for any value of x.
Clear my choice
Question 19
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What is the value of the derivative for the given value of t?
f (t) = (2t − 5)(3t + 4); whent =
Answer:
1
2
-1
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Question 20
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Is the given piecewise function continuous at x = 0?
Select one:
a. Yes, since the piecewise function is defined at x = 0.
b. No, since the graphs of the sub-functions will not meet at x = 0.
c. Yes, since the graphs of the sub-functions meet at x = 0.
d. No, since the piecewise function is undefined at x = 0.
Clear my choice
◄ Equation of a Tangent Line
Jump to...
Week 006 Calculus I - Differentiation Formulas ►
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Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Evaluate the limit of:
−− 2
limx→3 [log(√3x )]
Answer:
0.23
Question 2
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Evaluate the limit of:
limx→− (x2 + 4x − 1)(x − 5)
1
3
Answer:
11.85
Question 3
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 3x − 7; atx = −14
Answer:
3
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Question 4
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Evaluate the limit of:
3 −
−−−−
limx→5 log3 √x2 + 4
Answer:
1.02
Question 5
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Evaluate the limit of:
3−
√x−1
limx→1 x−1
Answer:
0.3
Question 6
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = 2x2 + 4x; at(−2, 0)
Answer:
8
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Question 7
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 2 + x2 ; at(−1, 3)
Answer:
1
Question 8
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Is the given function continuous at x = 1?
f (x) = 2x2 − 3x + 1
Select one:
a. Yes, since the value of the function at x = 1 is 4.
b. No, since the value of the function at x = 1 is 4.
c. Yes, since the function is defined at x = 1.
d. No, since the function is undefined at x = 1.
Clear my choice
Question 9
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What is the slope of the tangent line at the given point?
y = x2 − 1; at(2, 3)
Answer:
4
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Question 10
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x2 ; at(2, 4)
Answer:
-4
Question 11
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x2 − 1; at(2, 3)
Answer:
4
Question 12
Answer saved
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = x3 + 3; at(1, 4)
Answer:
3
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Question 13
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
6
Question 14
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x2 + 4; at(−1, 5)
Answer:
1
Question 15
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Evaluate the limit of:
limy→−3 log2 3y 2
Answer:
4.75
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Question 16
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A wholesaler who sells a product by the kilo (or fraction of a kilo) charges PhP 100 per kg if
10 kilos or less are ordered. If more than 10 kg are ordered, the wholesaler charges PhP
1,000 plus PhP 70 for each kg in excess of 10 kg. Is there continuity with the function
resulting from this selling strategy of the wholesaler?
Select one:
a. The resulting piecewise function is not continuous since the graphs of its sub-functions will not meet exactly at x = 10 kg.
b. The resulting piecewise function is continuous since it will always be defined for any value of x.
c. The resulting piecewise function is not continuous since there are restrictions to its domain values.
d. The resulting piecewise function is continuous since the graphs of its sub-functions will meet at a specific value of x.
Clear my choice
Question 17
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Evaluate the limit of:
1
1
x−4
limx→4 x−4
Answer:
-0.08
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Question 18
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Is the given function continuous at x = 1?
f (x) =
x2 −1
x−1
Select one:
a. No, since the function is undefined at x = 1.
b. No, since the function has a value of 2 at x = 1.
c. Yes, since the function is defined at x = 1.
d. Yes, since the function has a value of 2 at x = 1.
Clear my choice
Question 19
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Is the given piecewise function continuous at x = 0?
Select one:
a. No, since the graphs of the sub-functions will not meet at x = 0.
b. Yes, since the piecewise function in defined at x = 0.
c. No, since the piecewise function is undefined at x = 0.
d. Yes, since the graphs of the sub-functions will meet at x = 0.
Clear my choice
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Question 20
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What is the slope of the tangent line at the given point?
y = 2x−2 ; at(1, 2)
Answer:
-4
◄ Equation of a Tangent Line
Jump to...
Week 006 Calculus I - Differentiation Formulas ►
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = x2 − 1; at(2, 3)
Answer:
-5
Question 2
Answer saved
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What is the largest interval (or union of intervals) on which the function below is
continuous?
f (x) =
√
−−−−−
25−x2
x−3
Select one:
a. The interval from negative 5 up to positive 5.
b. The interval that includes negative 5, positive 3, and positive 5.
c. The interval that excludes negative 5, positive 3, and positive 5.
d. The interval from negative 5 up to positive 5, without 3.
Clear my choice
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Question 3
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Is the given function continuous for x greater than or equal to 1?
−−
f (x) = x2 √−
x−
+6
Select one:
a. Yes, since the function can be graphed using analytical methods.
b. No, since the function will be undefined for some values of x.
c. Yes, since the function will always be defined for any value of x.
d. No, since the function can be graphed using a table of values only.
Clear my choice
Question 4
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Evaluate the limit of:
limx→2 (
Answer:
x+3
)
x2 +x+5
0.45
Question 5
Answer saved
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Evaluate the limit of:
√
(limx→2 )
Answer:
−
−
−2
x
5
25
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Question 6
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What is the value of the derivative for the given value of x?
f (x) = x4 − 5 + x−2 + 4x−4 ; x = −1
Answer:
14
Question 7
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 1 − x3 ; at(2, −7)
Answer:
-7
Question 8
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Check the continuity of the piecewise function below for x = 3 and x = -3.
Select one:
a. The piecewise function is not continuous at both at x = 3 and x = -3 since it is undefined for the said values of x.
b. The piecewise function is continuous at x = 3 since it is defined for this value of x. However, it is not continuous at x = -3 since it is
undefined for the said value of the domain.
c. The piecewise function is continuous at both at x = 3 and x = -3 since it is defined for the said values of x.
d. The piecewise function is continuous at x = -3 since it is defined for this value of the domain. However, it is not continuous at x = 3 since it is
undefined for the said value of x.
Clear my choice
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Question 9
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What is the slope of the tangent line at the given point?
y = 2 + x2 ; at(−1, 3)
Answer:
-2
Question 10
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 1 − x3 ; at(2, −7)
Answer:
-12
Question 11
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Evaluate the limit of:
limx→ 1 (x + 2)(x2 − 3x + 1)
2
Answer:
-0.625
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Question 12
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
x2 − y 2
Answer:
= 7; at(4, −3)
0
Question 13
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Is the given function continuous at x = 1?
f (x) =
1
x−1
Select one:
a. Yes, since the function is defined at x = 1.
b. No, since the value of the function at x = 1 is 1 over 0.
c. Yes, since the value of the function at x = 1 is 1 over 0.
d. No, since the function is undefined at x = 1.
Clear my choice
Question 14
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What is the slope of the tangent line at the given point?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
-1
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Question 15
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Evaluate the limit of:
limx→2
Answer:
√
−
−
x−
−1
x+2
0.5
Question 16
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = 42 − 4x + 1; atx = 1
Answer:
1
Question 17
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
3
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Question 18
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Is the function below continuous at x = 3?
f (x) =
x2 +4x+3
x+3
Select one:
a. The function is continuous at x = 3 since it has a value of 4 upon substituting x with 3.
b. The function is not continuous at x = 3 since it has no value at the said value of x.
c. The function is continuous at x = 3 since it can be graphed using a single line.
d. The function is continuous at x = 3 since it will yield a defined value at the said value of x.
Clear my choice
Question 19
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What is the value of the derivative for the given value of x?
f (x) = 6x5 + 3x4 − 2x3 + 5x2 − 8x + 9; x = −2
Answer:
332
Question 20
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Evaluate the limit of:
limx→−2
Answer:
x3 −x2 −x+10
x2 +3x+2
-15
◄ Equation of a Tangent Line
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Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Evaluate the limit of:
limx→4 (log2 3 + log2
Answer:
x2 )
5.58
Question 2
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x2 + 4; at(−1, 5)
Answer:
-1
Question 3
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
-1
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Question 4
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Is the given function continuous for all real numbers?
−
2 −−
f (x) = √−
x−
+1
Select one:
a. Yes, since the function will always be defined for any value of x.
b. Yes, since analytical methods can be used to graph the function.
c. No, since the function will be undefined for some values of x.
d. No, since the function's graph can only be generated using a table of values.
Clear my choice
Question 5
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Evaluate the limit of:
limx→0
sin3x
x
The given angle is in radians.
Answer:
3
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Question 6
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Is the given function continuous at x = 5?
f (x) =
–
−
√x−√5
x−5
Select one:
a. No, since the value of the function at x = 5 is 0.22.
b. Yes, since the function is defined at x = 5.
c. No, since the function is undefined at x = 5.
d. Yes, since the value of the function at x = 5 is 0.22.
Clear my choice
Question 7
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Evaluate the limit of:
limx→ π
4
sin x+cos x
tan x
The given angle is in radians.
Answer:
1.41
Question 8
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 2x−2 ; at(1, 2)
Answer:
1
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Question 9
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What is the value of the derivative for the given value of x?
y = (4.34)x2 + (0.98)x; whenx = −4
Answer:
-33.74
Question 10
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Is the given piecewise function continuous for the defined interval?
Select one:
a. No, since the graphs of the sub-functions will not meet.
b. Yes, since the piecewise function will always be defined for any value of x.
c. Yes, since the graphs of the sub-functions have a common point.
d. No, since the piecewise function will be undefined for some values of x.
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Question 11
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Is the given piecewise function continuous for the defined interval?
Select one:
a. Yes, since the graphs of the sub-functions will meet at x = 0.
b. No, since there are some values of x where the piecewise function will be undefined.
c. No, since the graphs of the sub-functions do not have a common point.
d. Yes, since the piecewise function will always be defined within the interval.
Clear my choice
Question 12
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Is the given piecewise function continuous for the defined interval?
Select one:
a. Yes, since the graphs of the sub-functions will meet at some points within the interval.
b. Yes, since the piecewise function is defined for all values within the interval.
c. No, since the graphs of the sub-functions will not meet within the interval.
d. No, since the piecewise function is undefined for some values within the interval.
Clear my choice
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Question 13
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Evaluate the limit of:
limx→3 log2 3x
Answer:
3.17
Question 14
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Consider the function below. Is this continuous for all real numbers?
1
f (x) = x−2
Select one:
a. The function is continuous since it can yield both positive and negative values.
b. The function is not continuous for all real numbers since there are restrictions for its domain values.
c. The function is not continuous for all real numbers since it can yield negative values.
d. The function is not continuous since its graph is aysmptotic to the x-axis.
Clear my choice
Question 15
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Evaluate the limit of:
x2 −1
limx→1 x−1
Answer:
2
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Question 16
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Evaluate the limit of:
limt→0 sint22 3t
The given angle is in radians.
Answer:
9
Question 17
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 42 − 4x + 1; atx = 1
Answer:
1
Question 18
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Is the given piecewise function continuous at x = -2?
Select one:
a. Yes, since the piecewise function is defined at x = -2.
b. No, since the piecewise function is undefined at x = -2.
c. Yes, since the graphs of the sub-functions will meet at x = -2.
d. No, since the graphs of the sub-functions will not meet at x = -2.
Clear my choice
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Question 19
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Is the given piecewise function continuous at x = 0?
Select one:
a. No, since the piecewise function is undefined at x = 0.
b. No, since the graphs of the sub-functions will not meet at x = 0.
c. Yes, since the piecewise function is defined at x = 0.
d. Yes, since the graphs of the sub-functions will meet at x = 0.
Clear my choice
Question 20
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What is the value of the derivative for the given value of t?
f (t) =
Answer:
1
6t3
;t = 5
-0.0008
◄ Equation of a Tangent Line
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Is the given function continuous at x = 0?
f (x) =
−−−−
−
√x+16−4
x
Select one:
a. Yes, since the function is defined at x = 0.
b. Yes, since the function has a value of 0.13 at x = 0.
c. No, since the function is undefined at x = 0.
d. No, since the function has a value of 0.13 at x = 0.
Clear my choice
Question 2
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Check the continuity of the piecewise function below for x = 3 and x = -3.
Select one:
a. The piecewise function is continuous at x = 3 since it is defined for this value of x. However, it is not continuous at x = -3 since it is
undefined for the said value of the domain.
b. The piecewise function is continuous at both at x = 3 and x = -3 since it is defined for the said values of x.
c. The piecewise function is continuous at x = -3 since it is defined for this value of the domain. However, it is not continuous at x = 3 since it is
undefined for the said value of x.
d. The piecewise function is not continuous at both at x = 3 and x = -3 since it is undefined for the said values of x.
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Question 3
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Is the given function continuous at x = 5?
f (x) =
–
−
√x−√5
x−5
Select one:
a. No, since the value of the function at x = 5 is 0.22.
b. Yes, since the function is defined at x = 5.
c. Yes, since the value of the function at x = 5 is 0.22.
d. No, since the function is undefined at x = 5.
Clear my choice
Question 4
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Evaluate the limit of:
limx→4 (log2 3 + log2
Answer:
x2 )
5.58
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Question 5
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Is the given function continuous at x = 4?
f (x) =
1
x−
1
4
x−4
Select one:
a. Yes, since the value of the function at x = 4 is -0.06.
b. Yes, since the function is defined at x = 4.
c. No, since the function is undefined at x = 4.
d. No, since the value of the function at x = 4 is -0.06.
Clear my choice
Question 6
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What is the slope of the tangent line at the given point?
y = 2x−2 ; at(1, 2)
Answer:
-4
Question 7
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 2 + x2 ; at(−1, 3)
Answer:
1
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Question 8
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Evaluate the limit of:
−− 2
limx→3 [log(√3x )]
Answer:
0.23
Question 9
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What is the slope of the tangent line at the given point?
y = x3 + 3; at(1, 4)
Answer:
3
Question 10
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = 2x2 + 4x; at(−2, 0)
Answer:
-4
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Question 11
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = x3 + 2x; atx = 0
Answer:
0
Question 12
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Evaluate the limit of:
3 −
−−−−
limx→5 log3 √x2 + 4
Answer:
1.02
Question 13
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What is the value of the derivative for the given value of x?
y = (4.34)x2 + (0.98)x; whenx = −4
Answer:
-33.74
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Question 14
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What is the slope of the tangent line at the given point?
y = 9 − x2 ; at(2, 5)
Answer:
-4
Question 15
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Find the general equation of the line tangent to the equation below at the given point.
What is the value of the constant in the equation of the tangent line?
y = x2 − 1; at(2, 3)
Answer:
4
Question 16
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = x2 − 6x + 9; at(3, 0)
Answer:
0
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Question 17
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
y = x2 + 4; at(−1, 5)
Answer:
-1
Question 18
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Evaluate the limit of:
limx→−1 3
Answer:
−−−−−−−−
√x2 −3x+1
6.71
Question 19
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What is the value of the derivative for the given value of r?
\(\Large f(r) = \frac {4}{3} \pi r^3; r = 6
Answer:
4
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Question 20
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Evaluate the limit of:
limx→2 x2x−63−4x+8
Answer:
0
◄ Equation of a Tangent Line
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Long Quiz 001
Home / My courses / BAED-BUSC2112-2022S / Week 5: Derivative of Functions / Long Quiz 001
Question 1
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Evaluate the limit of:
x−3
limx→3 √−
−−− −−−−
x−−2
√4−x
Answer:
1
Question 2
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Is the given piecewise function continuous at x = 2?
Select one:
a. Yes, since the piecewise function has a value at x = 2.
b. No, since the graphs of the sub-functions will not meet at x = 2.
c. Yes, since the graphs of the sub-functions will meet at x = 2.
d. No, since the sub-function already defined that the function is undefined at x = 2.
Clear my choice
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Question 3
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Evaluate the limit of:
limx→3 (
Answer:
−−
√3x
−
−
−
x√x−+1
)
0.5
Question 4
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What is the slope of the tangent line at the given point?
y = x3 − 6x2 + 8x; at(3, −3)
Answer:
-1
Question 5
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What is the slope of the tangent line at the given point?
y = x2 ; at(2, 4)
Answer:
4
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Question 6
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Evaluate the limit of:
limt→0
sin2 3t
t2
The given angle is in radians.
Answer:
9
Question 7
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of x in the equation of the tangent line?
x2 − y 2
Answer:
= 7; at(4, −3)
0
Question 8
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Find the general equation of the line tangent to the equation below at the given point.
What is the coefficient of y in the equation of the tangent line?
y = 42 − 4x + 1; atx = 1
Answer:
1
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Question 9
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Is the given function continuous at x = 4?
f (x) =
x2 −4
x−2
Select one:
a. Yes, since the function is defined at x = 4.
b. Yes, since the value of the function at x = 4 is 6.
c. No, since the value of the function at x = 4 is 6.
d. No, since the function is not defined at x = 4.
Clear my choice
Question 10
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What is the value of the derivative for the given value of x?
f (x) = 1 − 2x − x2 ; atx = 4
Answer:
-10
Question 11
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What is the value of the derivative for the given value of x?
f (x) = 13 x3 − x + 2; x = 3
Answer:
0.3
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Question 12
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Evaluate the limit of:
−−−−−−−−
limx→−1 (x2 + 2)√x2 + x + 5
Answer:
6. 71
Question 13
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Evaluate the limit of:
limx→0
sec x−1
x
The given angle is in radians.
Answer:
0
Question 14
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Evaluate the limit of:
limy→−3 log2 3y 2
Answer:
4.75
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Question 15
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Evaluate the limit of:
limz→4 log
Answer:
√zz
5
−
−−−
4−3 2
+1
0.14344
Question 16
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Evaluate the limit of:
−−−−
limx→3 (x2 √x + 6 )
Answer:
27
Question 17
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Evaluate the limit of:
limx→2
Answer:
–
−
√x−√2
x−2
0.14344
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Question 18
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What is the value of the derivative for the given value of x?
f (x) =
Answer:
x3
3
+
3
x3
;x = 2
0
Question 19
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Is the given function continuous for all real numbers?
−
2 −−
f (x) = √−
x−
+1
Select one:
a. Yes, since analytical methods can be used to graph the function.
b. No, since the function will be undefined for some values of x.
c. No, since the function's graph can only be generated using a table of values.
d. Yes, since the function will always be defined for any value of x.
Clear my choice
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Long Quiz 001
Question 20
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Is the given function continuous for all real numbers?
f (x) =
2
x2 −x
Select one:
a. Yes, since the function is always defined for any real number.
b. No, since the function cannot have some values in its domain.
c. Yes, since the function can be graphed using analytical methods.
d. No, since the function can only be graphed using a table of values.
Clear my choice
◄ Equation of a Tangent Line
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Week 006 Calculus I - Differentiation Formulas ►
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