Question 1

Determine whether f is continuous at c.
-$$f ( x ) = \frac { x + 2 } { x - 7 } ; c = 0$$

Accepted Answer

A)  continuous 
B)  not continuous 
A)  continuous 
B)  not continuous

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-An explosion causes debris to rise vertically with an initial velocity of 96 feet per second. The function $s ( t ) = - 16 t ^ { 2 } + 96 t$ describes the height of the debris above the ground, $s ( t )$, in feet, $t$ seconds after the explosion. What is the instantaneous speed of the debris $4.8$ second(s) after the explosion?

Accepted Answer

A)  $153.6 \mathrm { ft } / \mathrm { sec }$ 
B)  $- 57.6 \mathrm { ft } / \mathrm { sec }$ 
C)  $57.6 \mathrm { ft } / \mathrm { sec }$ 
D)  $- 153.6 \mathrm { ft } / \mathrm { sec }$ 
A)  $153.6 \mathrm { ft } / \mathrm { sec }$ 
B)  $- 57.6 \mathrm { ft } / \mathrm { sec }$ 
C)  $57.6 \mathrm { ft } / \mathrm { sec }$ 
D)  $- 153.6 \mathrm { ft } / \mathrm { sec }$

Question 3

Find the derivative of the function at the given value of x.
-$$f ( x ) = x ^ { 3 } + 4 x ; x = - 2$$

Accepted Answer

A)  $- 2$ 
B)  4 
C)  16 
D)  12 
A)  $- 2$ 
B)  4 
C)  16 
D)  12

Question 4

Use the graph of y = g(x) to answer the question.  
-Find $f ( - 1 )$.

Accepted Answer

A)  1 
B)  0 
C)  4 
D)  $- 1$ 
A)  1 
B)  0 
C)  4 
D)  $- 1$

Question 5

Find the limit algebraically.
-$$\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } - 4 } { x + 2 }$$

Accepted Answer

A)  Does not exist 
B)  $- 2$ 
C)  1 
D)  $- 4$ 
A)  Does not exist 
B)  $- 2$ 
C)  1 
D)  $- 4$

Question 6

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{array} { r l } 
- 2 x + 9 , & x  1
\end{array} ; \quad c = 1 \right.$$

Accepted Answer

A)  not continuous 
B)  continuous 
A)  not continuous 
B)  continuous

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-An explosion causes debris to rise vertically with an initial velocity of 112 feet per second. The function $s ( t ) = - 16 t ^ { 2 } + 112 t$ describes the height of the debris above the ground, $s ( t )$, in feet, $t$ seconds after the explosion. What is the instantaneous speed of the debris when it hits the ground?

Accepted Answer

A)  224 
B)  $- 224$ 
C)  $- 112$ 
D)  112 
A)  224 
B)  $- 224$ 
C)  $- 112$ 
D)  112

Question 8

Choose the one alternative that best completes the statement or answers the question.
Approximate the area under the curve and above the x-axis using n rectangles. Let the height of each rectangle be given
by the value of the function at the right side of the rectangle.
-$$f ( x ) = x ^ { 2 } \text { from } x = 0 \text { to } x = 4 ; n = 4$$

Accepted Answer

A)  27 
B)  33 
C)  36 
D)  30 
A)  27 
B)  33 
C)  36 
D)  30

Question 9

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )$$

Accepted Answer

A)  $- 5$ 
B)  0 
C)  5 
D)  does not exist 
A)  $- 5$ 
B)  0 
C)  5 
D)  does not exist

Question 10

Determine whether f is continuous at c.
-$$f ( x ) = \frac { x ^ { 2 } - 36 } { x - 6 } ; \quad c = 6$$

Accepted Answer

A)  continuous 
B)  not continuous 
A)  continuous 
B)  not continuous

Question 11

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The volume of a right cylindrical cone of height $6 \mathrm {~cm}$ and radius $\mathrm { r } \mathrm { cm }$ is $\mathrm { V } ( \mathrm { r } ) = 2 \pi \mathrm { r } ^ { 2 } \mathrm { cubic }$ centimeters (cm). Find the instantaneous rate of change of the volume with respect to the radius $\mathrm { r } w h e n \mathrm { r } = 4 \mathrm {~cm}$.

Accepted Answer

A)  $16 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$ 
B)  $16 \mathrm {~cm} ^ { 3 } / \mathrm { cm }$ 
C)  $4 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$ 
D)  $32 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$ 
A)  $16 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$ 
B)  $16 \mathrm {~cm} ^ { 3 } / \mathrm { cm }$ 
C)  $4 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$ 
D)  $32 \pi \mathrm { cm } ^ { 3 } / \mathrm { cm }$

Question 12

Write the word or phrase that best completes each statement or answers the question.
-(a) What area does the integral $\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }$ represent?
(b) Use a graphing utility to approximate the area to three decimal places.

Accepted Answer

(a) The ar

Question 13

Use the graph shown to determine if the limit exists. If it does, find its value.
-$\lim _ { x \rightarrow 8 } f ( x )$

Accepted Answer

A)  4 
B)  3 
C)  5 
D)  does not exist 
A)  4 
B)  3 
C)  5 
D)  does not exist

Question 14

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = 3 x - 1$$

Accepted Answer

A)  continuous for all real numbers 
B)  continuous for all real numbers except $x = 1$ 
C)  continuous for all real numbers except $x = \frac { 1 } { 3 }$ 
D)  continuous for all real numbers except $x = - \frac { 1 } { 3 }$ 
A)  continuous for all real numbers 
B)  continuous for all real numbers except $x = 1$ 
C)  continuous for all real numbers except $x = \frac { 1 } { 3 }$ 
D)  continuous for all real numbers except $x = - \frac { 1 } { 3 }$

Question 15

Write the word or phrase that best completes each statement or answers the question.
-$$f ( x ) = 4 x ^ { 3 } - 6 x + 2 ; x = - 4$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{array} { c l } 
\frac { 1 } { x - 2 } , & x > 2 \
x ^ { 2 } + 5 x , & x \leq 2
\end{array} ; \quad c = 2 \right.$$

Accepted Answer

A)  not continuous 
B)  continuous 
A)  not continuous 
B)  continuous

Question 17

Choose the one alternative that best completes the statement or answers the question.
-$$f ( x ) = \sin ( 8 x ) ; x = 7$$

Accepted Answer

A)  $6.8257$ 
B)  $521.5343$ 
C)  $- 6.8257$ 
D)  $- 521.5343$ 
A)  $6.8257$ 
B)  $521.5343$ 
C)  $- 6.8257$ 
D)  $- 521.5343$

Question 18

Find the limit algebraically.
-$$\lim _ { x \rightarrow 4 } \left( 4 x ^ { 3 } - 2 x + 123 \right) ^ { 2 / 3 }$$

Accepted Answer

A)  $- 125$ 
B)  $- 5$ 
C)  125 
D)  25 
A)  $- 125$ 
B)  $- 5$ 
C)  125 
D)  25

Question 19

Find the limit algebraically.
-$$\lim _ { x \rightarrow 6 } \frac { x + 6 } { ( x - 6 ) ^ { 2 } }$$

Accepted Answer

A)  0 
B)  6 
C)  Does not exist 
D)  $- 6$ 
A)  0 
B)  6 
C)  Does not exist 
D)  $- 6$

Question 20

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \left\{ \begin{aligned}
7 x & \text { if } x  6
\end{aligned} \right.$$

Accepted Answer

A)  continuous for all real numbers 
B)  continuous for all real numbers except $x = 7 , x = 6$ 
C)  continuous for all real numbers except $x = 6$ 
D)  continuous for all real numbers except $x = 0 , x = 6$ 
A)  continuous for all real numbers 
B)  continuous for all real numbers except $x = 7 , x = 6$ 
C)  continuous for all real numbers except $x = 6$ 
D)  continuous for all real numbers except $x = 0 , x = 6$

Determine whether f is continuous at c. - $f ( x ) = \frac { x + 2 } { x - 7 } ; c = 0$

Find the derivative of the function at the given value of x. - $f ( x ) = x ^ { 3 } + 4 x ; x = - 2$

Use the graph of y = g(x) to answer the question. -Find $f ( - 1 )$ .

Find the limit algebraically. - $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } - 4 } { x + 2 }$

Determine whether f is continuous at c. - $f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.$

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )$

Determine whether f is continuous at c. - $f ( x ) = \frac { x ^ { 2 } - 36 } { x - 6 } ; \quad c = 6$

Write the word or phrase that best completes each statement or answers the question. -(a) What area does the integral $\int _ { 0 } ^ { \pi / 2 } \sin x \cos x \mathrm { dx }$ represent? (b) Use a graphing utility to approximate the area to three decimal places.

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 8 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 8 } f ( x )$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = 3 x - 1$

Write the word or phrase that best completes each statement or answers the question. - $f ( x ) = 4 x ^ { 3 } - 6 x + 2 ; x = - 4$

Determine whether f is continuous at c. - $f ( x ) = \left\{ \begin{array} { c l } \frac { 1 } { x - 2 } , & x > 2 \\x ^ { 2 } + 5 x , & x \leq 2\end{array} ; \quad c = 2 \right.$

Choose the one alternative that best completes the statement or answers the question. - $f ( x ) = \sin ( 8 x ) ; x = 7$

Find the limit algebraically. - $\lim _ { x \rightarrow 4 } \left( 4 x ^ { 3 } - 2 x + 123 \right) ^ { 2 / 3 }$

Find the limit algebraically. - $\lim _ { x \rightarrow 6 } \frac { x + 6 } { ( x - 6 ) ^ { 2 } }$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \left\{ \begin{aligned}7 x & \text { if } x < 6 \\41 & \text { if } x = 6 \\x ^ { 2 } + 6 & \text { if } x > 6\end{aligned} \right.$

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 13: A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Determine whether f is continuous at c. - f(x)=x+2x−7;c=0f ( x ) = \frac { x + 2 } { x - 7 } ; c = 0f(x)=x−7x+2​;c=0

Find the derivative of the function at the given value of x. - f(x)=x3+4x;x=−2f ( x ) = x ^ { 3 } + 4 x ; x = - 2f(x)=x3+4x;x=−2

Use the graph of y = g(x) to answer the question. -Find f(−1)f ( - 1 )f(−1) .

Find the limit algebraically. - lim⁡x→2x2−4x+2\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } - 4 } { x + 2 }limx→2​x+2x2−4​

Determine whether f is continuous at c. - f(x)={−2x+9,x<1−7x+14,x>1;c=1f ( x ) = \left\{ \begin{array} { r l } - 2 x + 9 , & x < 1 \\- 7 x + 14 , & x > 1\end{array} ; \quad c = 1 \right.f(x)={−2x+9,−7x+14,​x<1x>1​;c=1

Find the limit algebraically. - lim⁡x→0(x−5)(x+5)\lim _ { x \rightarrow 0 } ( x - \sqrt { 5 } ) ( x + \sqrt { 5 } )limx→0​(x−5​)(x+5​)

Determine whether f is continuous at c. - f(x)=x2−36x−6;c=6f ( x ) = \frac { x ^ { 2 } - 36 } { x - 6 } ; \quad c = 6f(x)=x−6x2−36​;c=6

Use the graph shown to determine if the limit exists. If it does, find its value. - lim⁡x→8f(x)\lim _ { x \rightarrow 8 } f ( x )limx→8​f(x)

Find the numbers at which f is continuous. At which numbers is f discontinuous? - f(x)=3x−1f ( x ) = 3 x - 1f(x)=3x−1

Write the word or phrase that best completes each statement or answers the question. - f(x)=4x3−6x+2;x=−4f ( x ) = 4 x ^ { 3 } - 6 x + 2 ; x = - 4f(x)=4x3−6x+2;x=−4

Determine whether f is continuous at c. - f(x)={1x−2,x>2x2+5x,x≤2;c=2f ( x ) = \left\{ \begin{array} { c l } \frac { 1 } { x - 2 } , & x > 2 \\x ^ { 2 } + 5 x , & x \leq 2\end{array} ; \quad c = 2 \right.f(x)={x−21​,x2+5x,​x>2x≤2​;c=2

Choose the one alternative that best completes the statement or answers the question. - f(x)=sin⁡(8x);x=7f ( x ) = \sin ( 8 x ) ; x = 7f(x)=sin(8x);x=7

Find the limit algebraically. - lim⁡x→4(4x3−2x+123)2/3\lim _ { x \rightarrow 4 } \left( 4 x ^ { 3 } - 2 x + 123 \right) ^ { 2 / 3 }limx→4​(4x3−2x+123)2/3

Find the limit algebraically. - lim⁡x→6x+6(x−6)2\lim _ { x \rightarrow 6 } \frac { x + 6 } { ( x - 6 ) ^ { 2 } }limx→6​(x−6)2x+6​