11/19/2019
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
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MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20
INSTRUCTOR
Justin Thomas
1.6 Limits at Infinity (Homework)
Springfield Public Schools.MO
Current Score
QUESTION
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
POINTS
3/3
3/3
3/3
3/3
3/3
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
1/1
2/2
TOTAL SCORE
31/31
100.0%
Due Date
JUNE 13
10:59 PM CDT
Request Extension
Assignment Submission & Scoring
Assignment Submission
For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only
changes if you submit or change the answer.
Assignment Scoring
Your last submission is used for your score.
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1/11
11/19/2019
1.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
3/3 points
Previous Answers
LarHSCalc1 1.6.019.MI.SA.
My Notes
Ask Your Teacher
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any
points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Find the limit.
lim
6+
x→∞
3
x
Step 1
Recall from Theorem 3.10 that if r is a positive rational number and c is any real number, then
lim
c
r
x→∞ x
= 0
0 .
Step 2
Using Theorem 3.10 along with Property of limits,
lim
x→∞
6+
3
x
= lim 6 + lim
x→∞
x→∞
3
x
= 6+ 0
= 6
0
6 .
You have now completed the Master It.
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11/19/2019
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
3/3 points
2.
Previous Answers
LarHSCalc1 1.6.021.MI.SA.
My Notes
Ask Your Teacher
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any
points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
Find the limit.
lim
x→∞
11x − 4
12x + 6
Step 1
The degree of the numerator is equal to
equal to the degree of the denominator.
Step 2
Therefore the limit is equal to the ratio of the leading coefficients.
is equal to the ratio of the leading coefficients.
Step 3
11x − 4
=
12x + 6
$$1112
lim
x→∞
Thus,
.
You have now completed the Master It.
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3/11
11/19/2019
3.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
3/3 points
Previous Answers
LarHSCalc1 1.6.014.
My Notes
Ask Your Teacher
Find the given limits, if possible.
f(x) = 5x2 + 2x + 5
(a)
h(x) =
lim h(x) =
f(x)
x
x→∞
dne
(b)
h(x) =
lim h(x) =
f(x)
x2
x→∞
5
(c)
h(x) =
lim h(x) =
f(x)
x3
x→∞
0
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4/11
11/19/2019
4.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
3/3 points
Previous Answers
LarHSCalc1 1.6.016.
My Notes
Ask Your Teacher
Find each limit, if possible.
(a)
lim
x→∞
8 − 5x
8x3 − 6
=
0
(b)
lim
x→∞
8 − 5x
=
8x − 6
−58
(c)
lim
x→∞
8 − 5x2 =
8x − 6
dne
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5.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
3/3 points
Previous Answers
LarHSCalc1 1.6.018.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.020.
My Notes
Ask Your Teacher
Find each limit if possible.
(a)
lim
x→∞
7x3/2
2x2 + 5
=
0
(b)
lim
x→∞
7x3/2
2x3/2 + 5
=
72
(c)
lim
x→∞
7x3/2
2
x +5
=
dne
6.
1/1 points
Previous Answers
Find the limit.
lim
x → −∞
6
x
−
x
8
dne
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6/11
11/19/2019
7.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
1/1 points
Previous Answers
LarHSCalc1 1.6.021.MI.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.023.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.024.
My Notes
Ask Your Teacher
Find the limit.
lim
x→∞
2x − 8
3x + 1
23
8.
1/1 points
Previous Answers
Find the limit.
lim
4x5
x → ∞ x5 − 6
4
9.
1/1 points
Previous Answers
Find the limit.
lim
9x3 + 1
x → −∞ 45x3 − 3x2 + 4
15
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7/11
11/19/2019
10.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
1/1 points
Previous Answers
LarHSCalc1 1.6.025.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.029.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.030.
My Notes
Ask Your Teacher
Find the limit.
x
lim
x2 − x
x→−∞
−1
1/1 points
11.
Previous Answers
Find the limit.
lim
x→∞
x2 − 2
6x−6
16
12.
1/1 points
Previous Answers
Find the limit.
lim
x → −∞
x14 − 1
x9 − 1
0
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8/11
11/19/2019
13.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
1/1 points
Previous Answers
LarHSCalc1 1.6.031.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.033.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.034.
My Notes
Ask Your Teacher
Find the limit.
lim
x→∞
x+9
(x2 + 8)1/3
dne
14.
1/1 points
Previous Answers
Find the limit.
lim
x→∞
4
2x + sin x
0
15.
1/1 points
Previous Answers
Find the limit.
lim 4 cos
x→∞
8
5x
4
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9/11
11/19/2019
16.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
1/1 points
Previous Answers
LarHSCalc1 1.6.035.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.036.
My Notes
Ask Your Teacher
LarHSCalc1 1.6.049.
My Notes
Ask Your Teacher
Find the limit.
lim
x→∞
sin(7 x)
x
0
17.
1/1 points
Previous Answers
Find the limit.
lim
x→∞
6x − cos x
x
6
18.
1/1 points
Previous Answers
Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.)
lim x sin
x→∞
5
x
5
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11/19/2019
19.
1.6 Limits at Infinity - MASTER - AP Calculus AB 19-20, section Calc AB (Sem 1) FA20 | WebAssign
1/1 points
Previous Answers
LarHSCalc1 1.6.050.MI.
My Notes
Ask Your Teacher
My Notes
Ask Your Teacher
Find the limit. (Hint: Let x = 1/t and find the limit as t → 0+.)
lim 4x tan
x→∞
5
x
20
20.
2/2 points
Previous Answers
LarHSCalc1 1.6.JIT.002.
Find all horizontal and vertical asymptotes (if any). (Enter your answers as a comma-separated list. If an answer does not exist,
enter DNE.)
r(x) =
6x3 − 2
2x3 + 5x2 + 9x
0
vertical asymptote(s)
x=
3
horizontal asymptote(s)
y=
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