What is the value of the derivative of the function below for t = 1? The given angle is in radians.
Use 3.141592654 for the value of pi.
S = sin ⟮4t + π3⟯ + sin ⟮4t + π6⟯
Answer: 0.56
Evaluate the limit of:
limx→5 x2-25/x−5
Answer: 10
What is the value of the constant in the line tangent to the equation below at the given point?
Consider the general form of the equation of the tangent line.
h(x) = √x+1; at (3, 2)
Answer: 5
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
y = tan 2x sec x + tan (2 sec x)
Answer: 14.41
Evaluate the limit of:
Lim x→4 (2x + 1)x
Answer: 6561
What is the slope of the line tangent to the equation below at the given point?
y = 2 / √x − 1; at x = 4
Answer: -0.13
Evaluate the limit of:
lim x → 1/2 (x + 2)(x2 − 3x + 1)
Answer: -0.63
What is the value of the derivative of the function below for x = 1?
y = 2x3 + 4/x2 + 1
Answer: 0
Evaluate:
lim x→4 3x2 − 17x + 20/4x2 − 25x + 36
Answer: 0.14344
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
y = 4 cos 3x – 3 sin 4x
Answer: 6.15
A rectangular field is to be fenced off along the bank of a river where no fence is required along
the bank. If the material for the fence costs Php 12.00 per running foot for the two ends and Php
18.00 per running foot for the side parallel to the river, find the width of the field (in feet) of the
largest possible area that can be enclosed with Php 5,400.00 worth of fence.
Answer: 112.5
What is the value of the derivative of the function below for x = 1?
f(x) = (x3 + 1/x2 + 3)(x2 − 2x-1 + 1)
Answer: 0.5
What is the value of the derivative of the function below for x = -1? The associated angle is in
radians.
y = sec e2x = e2 sec x
Answer: -233.52
What is the value of the derivative of the function below for y = 1?
g(y) = (7 – 3y)2
Answer: -24
What is the value of the derivative of the function below for x = -1?
f(x) = log10x/x
Answer: 0.14344
Is the given piecewise function continuous at x = -2?
Answer: No, since the graphs of the sub-functions will not meet at x = -2
What is the value of the derivative of the function below for x = -1? The given angle is in
radians.
y = e2 sin 3x
Answer: -4.48
What is the value of the derivative of the function below for x = 1?
f(x) = 3/x2 + 5/x4
Answer: -26
Is the given function continuous for all real numbers?
f(x) = x2(x + 3)2
Answer: The function is continuous for all real numbers since it will always have a defined
value
Is the function below continuous at x = -2?
Answer: The function is continuous at x = -2 since it has a defined value at x = -2
What is the value of the derivative of the function below for x = -1?
y = 25x34x2
Answer: -6.74
What is the value of the derivative of the function below for y = 1?
g(y) = 1/√25 – y2
Answer: 0.01
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
y = cos(3x2 + 1)
Answer: 4.54
What is the value of the derivative of the function below for x = 1?
f(x) = x5 – 1/15x5
Answer: 5.33
What is the value of the derivative of the function below for x = -1? The given angle is in
radians.
y = tan e3x + 3tan 3x
Answer: 3.68
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: -1
What is the value of the derivative of the function below for x = 1?
f(x) = (2x4 – 1)(5x3 + 6x)
Answer: 109
What is the value of the derivative of the function below for x = -1?
y = ln e4x – 1/e4x + 1
Answer: -0.15
What is the value of the derivative of the function below for x = -1? The associated angle is in
radians.
y = sin (ln(2x + 1))
Answer: 0.14344
Is the piecewise function below continuous at x = -3?
Answer: The piecewise function is not continuous since the graphs of its sub-functions will not
meet at x = -3
What is the value of the third derivative of the function below for x = 2? The given angle is in
radians.
f(x) = cos3 x
Answer: -1.58
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
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
y = tan x/1 + x
Answer: 1.32
What is the slope of the line tangent to the equation below at the given point?
f(x) = -8/√x; at (4, -4)
Answer: 0.5
Is the given piecewise function continuous for the defined interval?
Answer: No, since the graphs of the sub-functions will not meet within the interval
Evaluate:
lim y→−2 y3 + 8/y3 – 8
Answer: 0
Evaluate:
lim x→2 √x3 + 3x + 4/x3 + 1
Answer: 1.41
Evaluate:
lim x→−1 2x2 – x – 3/x3 + 1x2 + 6x + 5
Answer: -1
What is the coefficient of y in the line tangent to the equation below at the given point? Consider
the general form of the equation of the tangent line.
y = x2 – 6x + 9; at (3, 0)
Answer: 1
Is the function below continuous at x = -5?
f(x) = x3 - 2x2 + 5x + 1
Answer: The function is continuous since it is defined at the given value of x
Is the function below continuous for all real numbers?
f(x) = x3 + 1 / x2 – 9
Answer: The function is not continuous since there are restricted values for its domain
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
y = 1 + x2/sin x
Answer: 1.61
What is the value of the derivative of the function below for x = 1? The given angle is in radians.
f(x) = sin2 (cos 2x)
Answer: 1.34
What is the value of the derivative of the function below for x = 1?
g(x) = 3√4x2 – 1
Answer: 1.28
What is the value of the fourth derivative of the function below for x = 2?
f(x) = 2x7 – x5 + 5x3 – 8x + 4
Answer: 13200
What is the value of the derivative of the function below for t = 1?
f(t) = (t3 – 2t + 1)(2t2 + 3t)
Answer: 5
What is the value of the derivative of the function below for x = 1?
f(x) = 2x7 – x5 + 5x3 – 8x + 4
Answer: 16
Evaluate the limit of:
Lim x→3 (x2 √x + 6)
Answer: 27
Is the piecewise function below continuous for the given interval?
Answer: The piecewise function is not continuous since there is a "jump" in the graphs of its
sub-functions
Is the given piecewise function continuous for the defined interval?
Answer: Yes, since the graphs of the sub-functions will meet at a common point
What is the value of the derivative of the function below for x = -1?
f(x) = x√x
Answer: 0.14344
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 + 2x; at x = 0
Answer: 1
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?
Answer: The resulting piecewise function is not continuous since the graphs of its sub-functions
will not meet exactly at x = 10 kg
What is the value of the derivative for the given value of x?
y = x3 – 3x2 + 5x – 2; x = 7
Answer: 110
Evaluate the limit of:
lim x→√2 2x2 – 3x + 6/x2 + 2
Answer: 1.44
Evaluate:
lim h→0 √h + 2 - √2/h
Answer: 0.35
What is the value of the derivative of the function below for t = 1? The given angle is in radians.
y = 1/3 sec3 2t – sec 2t
Answer: -71.47
Is the given function continuous at x = 1?
f(x) = 1/x – 1
Answer: No, since the function is undefined at x = 1
What is the value of the derivative of the function below for x = -1?
y = ln (3x/x2 + 4)
Answer: -0.6
Is the given function continuous at x = 4?
f(x) = 1/x – ¼ / x – 4
Answer: Yes, since the function is defined at x = 4
Evaluate the limit of:
lim t → 0 sin23t / t2
The given angle is in radians.
Answer: 9
Evaluate the limit of:
lim x→0 1 – cos x/x
The given angle is in radians.
Answer: 0
Is the function below continuous for all real numbers?
f(x) = √x – 2/x – 4
Answer: The function is not continuous since there are real numbers that cannot be in its domain
Evaluate the limit of:
lim x→2 (x2 – 5x + 1)
Answer: -5
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 = 9 – x2; at (2, 5)
Answer: 1
Evaluate the limit of:
lim x→−1 3√x2−3x+1
Answer: 11.66
Check the continuity of the piecewise function below for x = 3 and x = -3
Answer: 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
What is the coefficient of x in the line tangent to the equation below at the given point? Consider
the general form of the equation of the tangent line.
f(x) = 4 / x2; at (2, 1)
Answer: 1
What is the value of the derivative for the given value of x?
y = 1/3 x3 + ½ x2 + x + 1; when x = 6.42
Answer: 48.64
Evaluate the limit of:
lim x→3 log2 3x
Answer: 3.17
Is the piecewise function below continuous at x = -3 or not?
Answer: The piecewise function is not continuous at x = -3 since the graphs of its sub-functions
do not meet at this value of x
Evaluate the limit of:
lim x→4 (log2 3 + log2 x2)
Answer: 5.58
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
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; at x = -14
Answer: 7
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: -3
Evaluate the limit of:
lim x→0 cos x/sin x – 3
The given angle is in radians.
Answer: -0.33
What is the value of the derivative for the given value of t?
f(t) = (t3 – 2t + 1)(2t2 + 3t); t = -3
Answer: 405
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 – y2 = 7; at (4, -3)
Answer: -4
Is the given function continuous for x greater than -2?
f(x) = 2x3 + 5x2 – 7
Answer: Yes, since the function will always be defined for any value of x
What is the slope of the tangent line at the given point?
y = x3 - 6x2 + 8x; at (3, -3)
Answer: -1
Evaluate the limit of:
lim x→−2 x3 - x2 – x + 10/x2 + 3x + 2
Answer: -15
Is the function below continuous for all real numbers?
f(x) = (x – 5)3 (x2 + 4)5
Answer: The function is continuous for all real numbers since it will always be defined for any
value of x
Evaluate the limit of:
lim y→−3 log2 3y2
Answer: 4.75
Is the given function continuous for all real numbers?
f(x) = √x2 + 1
Answer: Yes, since the function will always be defined for any value of x
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 – y2 = 7; at (4, -3)
Answer: 3
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 = 1 – x3; at (2, -7)
Answer: 11
Evaluate the limit of:
lim x→2 (34x e2x)
Answer: 358218.46
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; at (2, 4)
Answer: 4
What is the slope of the tangent line at the given point?
y = 2 + x2; at (-1, 3)
Answer: -2
Evaluate the limit of:
lim x→3 (x2 + 7x – 5)
Answer: 25
Is the given function continuous for all real numbers?
f(x) = x4 + 2x3 – 8x + 1
Answer: Yes, since the function will always be defined for any value of x
Evaluate the limit of:
lim x→2 (x + 3/x2 + x + 5)
Answer: 0.45
Is the given piecewise function continuous at x = 0?
Answer: No, since the graphs of the sub-functions will not meet at x = 0
What is the value of the derivative for the given value of x?
y = (4.34)x2 + (0.98)x; when x = -4
Answer: -33.74
Evaluate the limit of:
lim x→1 √x2 + 1
Answer: 1.41
Evaluate the limit of:
lim x→2 x2 + 2x – 8 / 5x – 10
Answer: 1.2
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
Evaluate the limit of:
lim x→0 sin3x / x
The given angle is in radians.
Answer: 3
Is the given piecewise function continuous at x = 0?
Answer: Yes, since the graphs of the sub-functions meet at x = 0
Is the given function continuous for all real numbers?
g(x) = x2 – 1/x – 1
Answer: Yes, since the function will always be defined for any value of x
What is the slope of the tangent line at the given point?
y = 2x-2; at (1, 2)
Answer: -4
Evaluate the limit of:
lim x→2 (2x3 + 5x2 – 7)
Answer: 29
Is the given function continuous at x = 1?
f(x) = x2 – 1/x – 1
Answer: Yes, since the function is defined at x = 1
Is the given piecewise function continuous for the defined interval?
Answer: No, since the graphs of the sub-functions will not meet
What is the value of the derivative for the given value of t?
f(t) = (2t – 5) (3t + 4); when t = ½
Answer: -1
Is the given function continuous at x = -3?
Answer: No, since the graphs of the sub-functions will not meet at x = -3 / No, since the
piecewise function is undefined at x = -3
What is the slope of the tangent line at the given point?
x2 – y2 = 7; at (4, -3)
Answer: 1.33
Evaluate the limit of:
lim x→−1 x2 + 9x + 8 / x2 + 4x + 3
Answer: 3.5
What is the value of the derivative for the given value of x?
3x3 + 2x2 + x + 5; when x = 3
Answer: 94
What is the slope of the tangent line at the given point?
y = x2; at (2, 4)
Answer: 4
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 = 9 – x2; at (2, 5)
Answer: 4
Evaluate the limit of:
lim x→1 x – 1/√x + 3 – 2
Answer: 4
What is the slope of the tangent line at the given point?
y = 9 – x2; at (2, 5)
Answer: -4
Is the given function continuous for x greater than -2?
f(x) = x2 – 1 / x – 1
Answer: Yes, since the function will always be defined for x greater than -2
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
What is the slope of the tangent line at the given point?
y = 42 – 4x + 1; at x = 1
Answer: 4
Is the function below continuous for all real numbers?
f(x) = x3 + 1/x2 – 9
Answer: The function is not continuous since there are restricted values for its domain
Evaluate the limit of:
lim x→−1 (x2 + 2) √x2 + x + 5
Answer: 6.71
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
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: -1
Is the given function continuous for all real numbers?
f(x) = x2(x + 3)2
Answer: The function is continuous for all real numbers since it will always have a defined
value
Is the given piecewise function continuous at x = 0?
Answer: No, since the graphs of the sub-functions will not meet at x = 0
Is the given function continuous at x = 4?
f(x) = x2 – 4 / x – 2
Answer: Yes, since the function is defined at x = 4
Is the given function continuous at x = 3?
Answer: Yes, since the graphs of the sub-functions will meet at x = 3
Evaluate the limit of:
lim x→1 (x2 + 3x – 4)
Answer: 0
Is the given piecewise function continuous at x = 0?
Answer: No, since the graphs of the sub-functions will not meet at x = 0
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; at x = 0
Answer: -2
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 = 3x – 7; at x = -14
Answer: 1
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
Evaluate the limit of:
lim x→1 (2/x)x^2
Answer: 2
Evaluate the limit of:
lim z→4 log 5√4 – 3z2/z + 1
Answer: 0.14344
Evaluate the limit of:
lim x→3 [log(√3x)]2
Answer: 0.23
Is the given function continuous for x greater than or equal to 1?
f(x) = x2 √x + 6
Answer: Yes, since the function will always be defined for any value of x
Is the given piecewise function continuous at x = 3?
Answer: Yes, since the graphs of the sub-functions will meet at x = 3
Evaluate the limit of:
(lim x→2) √5x^2
Answer: 25
Evaluate the limit of:
lim x→1 x2 – 1/x – 1
Answer: 2
Is the given function continuous at x = 0?
f(x) =√x + 16 - 4x / x
Answer: Yes, since the function is defined at x = 0
Is the function below continuous at x = 3?
f(x) = x2 + 4x + 3 / x + 3
Answer: The function is continuous at x = 3 since it will yield a defined value at the said value
of x
Evaluate the limit of:
lim x→4 1/x – ¼ / x – 4
Answer: -0.06
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: 1
Is the given function continuous for x greater than -3?
f(x) = (x2 + 2) √x2 + x + 5
Answer: Yes, since the function will always be defined for any value in the interval
What is the slope of the tangent line at the given point?
y = x2 + 4; at (-1, 5)
Answer: -2
What is the value of the derivative for the given value of x?
f(x) = x4 – 5 + x-2 + 4-4; x = -1
Answer: 14
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
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: 2
Evaluate the limit of:
lim x→1 3√x – 1/x – 1
Answer: 0.33
What is the value of the derivative for the given value of x?
f(x) = x3/3 + 3/x3; x = 2
Answer: 3.44
Evaluate the limit of:
lim x→π/4 sin x + cos x / tan x
The given angle is in radians.
Answer: 1.41
What is the value of the derivative for the given value of x?
f(x) = 1/3 x3 – x + 2; x = 3
Answer: 8
Evaluate the limit of:
lim x→2 log5 (4x3 + 5)
Answer: 2.24
Consider the function below. Is this continuous for all real numbers?
f(x) = 1 / x - 2
Answer: The function is not continuous for all real numbers since there are restrictions for its
domain values
What is the value of the derivative for the given value of x?
f(x) = 1 – 2x – x2; at x = 4
Answer: -10
Evaluate the limit of:
lim x→2 x2 − 6x + 8 / x3− 4
Answer: 0
Evaluate the limit of:
lim x→2 √x − √2 / x – 2
Answer: 0.14344
Evaluate the limit of:
lim r→1 √8r + 1 / r + 3
Answer: 1.5
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: 8
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: -15
Evaluate the limit of:
lim x→2 x2 – 1 / x – 1
Answer: 3
Evaluate the limit of:
lim x→−1 x3 + 1 / x + 1
Answer: 3
Is the given function continuous for all real numbers?
f(x) = 2 / x2 – x
Answer: No, since the function cannot have some values in its domain
Is the given function continuous for x less than 5?
f(x) = (x2 + 4x – 1)(x – 5)
Answer: Yes, since the function will always be defined for values of x less than 5
Evaluate the limit of:
lim x→3 x2 + x – 12 / x2 – 9
Answer: 1.17
Evaluate the limit of:
lim x→∞ (0.1x + 0.7x)
Answer: 0
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; at x = 0
Answer: 0
Evaluate the limit of:
lim x→4 3√x2 – 3x + 4 / 2x2 – x – 1
Answer: 0.67
Is the given piecewise function continuous at x = 2?
Answer: No, since the sub-function already defined that the function is undefined at x = 2
What is the value of the derivative for the given value of x?
y = x35; when x = 1
Answer: 35
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 – 1; at (2, 3)
Answer: -4
Evaluate the limit of:
lim x→0 cot 2x / csc x
The given angle is in radians.
Answer: 1
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 + 3; at (1, 4)
Answer: 1
What is the slope of the tangent line at the given point?
y = 2x2 + 4x; at (-2, 0)
Answer: -4
Is the given piecewise function continuous for the defined interval?
Answer: Yes, since the graphs of the sub-functions will meet at a point within the defined
interval
Is the given piecewise function continuous for the defined interval?
Answer: No, since the graphs of the sub-functions will not meet
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
Evaluate the limit of:
lim x→3 x − 3 / √x − 2 - √4 – x
Answer: 0.14344
Is the given piecewise function continuous at x = 1?
Answer: No, since the graphs of the sub-functions will not meet at x = 1
What is the slope of the tangent line at the given point?
y = 1 – x3; at (2, -7)
Answer: -11
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
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 = 2x2 + 4x; at (-2, 0)
Answer: 1
Evaluate the limit of:
lim x→2 (5x + 2x + 4)
Answer: 33
Is the given function continuous at x = 1?
f(x) = 2x2 – 3x + 1
Answer: Yes, since the function is defined at x = 1
Is the given function continuous at x = 2?
f(x) = x2 – 4 / x − 2
Answer: Yes, since the function is defined at x = 2
Evaluate the limit of:
Lim x→0 sec x − 1 / x
The given angle is in radians.
Answer: 0
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 = 9 – x2; at (2, 5)
Answer: -13
Evaluate the limit of:
lim x→0 √1 + x – 1 / x
Answer: 0.5
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 – 6x + 9; at (3, 0)
Answer: 1
Evaluate the limit of:
lim x→0 sin2 x / 2x
The given angle is in radians.
Answer: 1
Evaluate the limit of:
lim x→4 x3 – 64 / x2 – 16
Answer: 6
Is the given function continuous for all real numbers?
f(x) = (x + 4) / (x – 1)(x + 8)
Answer: No, since the function will be undefined at both x = 1 and x = -8
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?
x2 – y2 = 7; at (4, -3)
Answer: 25
Is the given function continuous for values less than 1?
g(x) = x2 – 1 / x – 1
Answer: Yes, since the function will always be defined within the interval
Is the given function continuous for all real numbers?
f(x) = x(x + 5)(x + 3) / (x + 5)(x + 1)
Answer: No, since the function will be undefined at x = -1 only
Evaluate the limit of:
lim x→−2 √x2 + 2x + 8
Answer: 2.83
Evaluate the limit of:
lim x→2 4x – 5
Answer: 3
Evaluate the limit of:
lim x→0 sin 5x / 2x
The given angle is in radians.
Answer: 2.5
What is the value of the derivative of the function below for x = 1?
f(x) = 2x7 – x5 + 5x3 – 8x + 4
Answer: 16
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
Evaluate the limit of:
lim x→3 e4x / e3x + 2
Answer: 20.08
Is the given piecewise function continuous for the defined interval?
Answer: No, since the graphs of the sub-functions will not meet within the interval
What is the value of the derivative for the given value of r?
f(r) = 4/3 π3; r = 6
Answer: 452.39
Find the general equation of the line tangent to the equation below at the given point.
What is the value of constant in the equation of the tangent line?
y = x2 + 4; at (-1, 5)
Answer: -3
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 = 42 – 4x + 1; at x = 1
Answer: -4
What is the value of the derivative for the given value of t?
f(t) = 1/6t3; t = 5
Answer: 0
Evaluate the limit of:
lim x→2 √x − 1 / x + 2
Answer: 0.5
Is the given piecewise function continuous at x = 3?
Answer: No, since the graphs of the sub-functions will not meet at x = 3
For what values of x is the function below continuous?
f(x) = x2 + 3x + 5 / x2 + 3x – 4
Answer: All real numbers except negative 4 and positive 1
What is the slope of the tangent line at the given point?
y = x3 + 3; at (1, 4)
Answer: 3
What is the slope of the tangent line at the given point?
y = x2 – 6x + 9; at (3, 0)
Answer: 0
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: 4
What is the largest interval (or union of intervals) on which the function below is continuous?
f(x) = √25 – x2 / x − 3
Answer: The interval from negative 5 up to positive 5, without 3
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 – 6x + 9; at (3, 0)
Answer: 0
Is the given piecewise function continuous at x = 3?
Answer: Yes, since the graphs of the sub-functions meet at x = 3
What is the slope of the tangent line at the given point?
y = 3x – 7; at x = -14
Answer: 3
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 + 2x; at x = 0
Answer: 1
Evaluate the limit of:
lim x→−1/3 (x2 + 4x – 1)(x – 5)
Answer: 10.37
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; at x = 1
Answer: 3
Evaluate the limit of:
lim x→2 √x3 + 2x + 3 / x2 + 5
Answer: 1.67
What is the slope of the tangent line at the given point?
y = x2 – 1; at (2, 3)
Answer: 4
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
Evaluate the limit of:
lim x→3 (√3x / x√x + 1)
Answer: 0.5
What is the value of the derivative for the given value of y?
f(y) = (y3 – 8 / y3 + 8); y = 2
Answer: 0.75
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; at x = 1
Answer: 1
Compute for the derivative of the given function for x = -1. The angle is in radians.
y = sec2 (x2 – 3)
Answer: -50.47
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: 0
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: 1
What is the value of the derivative for the given value of x?
f(x) = 6x5 + 3x4 – 2x3 + 5x2 – 8x + 9; at x = -2
Answer: 332
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
Evaluate the limit of:
lim x→5 log3 3√x2+4
Answer: 1.02