Question 1

Find the equation of the tangent line to the graph of f at the given point.
-$f ( x ) = x ^ { 2 } + 5 x$ at $( 4,20 )$

Accepted Answer

A)  $y = 2 x + 5$ 
B)  $y = 2 x - 5$ 
C)  $y = 13 x - 32$ 
D)  $y = 13 x - 72$ 
A)  $y = 2 x + 5$ 
B)  $y = 2 x - 5$ 
C)  $y = 13 x - 32$ 
D)  $y = 13 x - 72$

Question 2

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

Accepted Answer

A)  continuous for all real numbers except $x = - 3$ 
B)  continuous for all real numbers except $x = 0$ 
C)  continuous for all real numbers 
D)  continuous for all real numbers except $x = 1$ 
A)  continuous for all real numbers except $x = - 3$ 
B)  continuous for all real numbers except $x = 0$ 
C)  continuous for all real numbers 
D)  continuous for all real numbers except $x = 1$

Question 3

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } \frac { 2 \sin x } { 4 x }$$

Accepted Answer

A)  Does not exist 
B)  $\frac { 1 } { 9 }$ 
C)  1 
D)  0 
A)  Does not exist 
B)  $\frac { 1 } { 9 }$ 
C)  1 
D)  0

Question 4

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = 4 \tan x$$

Accepted Answer

A)  continuous for all real numbers except $x = 0$ 
B)  continuous for all real numbers except $x = \frac { k \pi } { 2 }$ where $\mathrm { k }$ is an odd integer 
C)  continuous for all real numbers except $x = \frac { k \pi } { 4 }$ where $\mathrm { k }$ is an odd integer 
D)  continuous for all real numbers 
A)  continuous for all real numbers except $x = 0$ 
B)  continuous for all real numbers except $x = \frac { k \pi } { 2 }$ where $\mathrm { k }$ is an odd integer 
C)  continuous for all real numbers except $x = \frac { k \pi } { 4 }$ where $\mathrm { k }$ is an odd integer 
D)  continuous for all real numbers

Question 5

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } \left( x ^ { 2 } - 5 \right)$$

Accepted Answer

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

Question 6

Find the one-sided limit.
-$$\lim _ { x \rightarrow - ^ { - } } ( 4 - 5 x )$$

Accepted Answer

A)  0 
B)  $- 1$ 
C)  4 
D)  does not exist 
A)  0 
B)  $- 1$ 
C)  4 
D)  does not exist

Question 7

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.
-$$f ( x ) = x ^ { 2 } - 3 x + 4 \text { from } x = 1 \text { to } x = 5 ; n = 4$$

Accepted Answer

A)  18 
B)  38 
C)  28 
D)  48 
A)  18 
B)  38 
C)  28 
D)  48

Question 8

Find the limit as x approaches c of the average rate of change of the function from c to x.
-$$c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10$$

Accepted Answer

A)  3 
B)  Does not exist 
C)  13 
D)  $\frac { 1 } { 3 }$ 
A)  3 
B)  Does not exist 
C)  13 
D)  $\frac { 1 } { 3 }$

Question 9

Choose the one alternative that best completes the statement or answers the question.
-Provide a graph that illustrates the area represented by the integral. $$\int _ { 2 } ^ { 3 } x ^ { 2 } d x$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 10

Determine whether f is continuous at c.
-$$f ( x ) = \frac { 5 } { x ^ { 2 } - 2 x } ; \quad c = 0$$

Accepted Answer

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

Question 11

Use the TABLE feature of a graphing utility to find the limit.
-$$\lim _ { d \rightarrow 3 } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)$$

Accepted Answer

A)  27 
B)  9 
C)  0 
D)  does not exist 
A)  27 
B)  9 
C)  0 
D)  does not exist

Question 12

Use the graph of y = g(x) to answer the question.  
-Find $\lim _ { x \rightarrow - 1 } g ( x )$.

Accepted Answer

A)  1 
B)  0 
C)  4 
D)  does not exist 
A)  1 
B)  0 
C)  4 
D)  does not exist

Question 13

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The volume $V$ of a right circular cylinder of height 2 and radius $r$ is $V ( r ) = 2 \pi r ^ { 2 }$. Find the instantaneous rate of change of volume with respect to radius $r$ when $r = 7$.

Accepted Answer

A)  $23 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
B)  $28 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
C)  $98 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
D)  $32 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
A)  $23 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
B)  $28 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
C)  $98 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$ 
D)  $32 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }$

Question 14

Choose the one alternative that best completes the statement or answers the question.
-What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ represent?

Accepted Answer

A)  $- 1$ 
B)  10 
C)  11 
D)  1 
A)  $- 1$ 
B)  10 
C)  11 
D)  1

Question 15

Write the word or phrase that best completes each statement or answers the question.
Find the derivative of the function at the given value of x using a graphing utility. If necessary, round to four decimal
places.
-$$f ( x ) = 4 x \cos x ; x = \frac { \pi } { 2 }$$

Accepted Answer

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

Question 16

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-Given the function $\mathrm { f }$ defined over the interval [a, b], graph the function indicating the area A under $\mathrm { f }$ from a to $b$. express the area $\mathrm { A }$ as an integral.
$$f ( x ) = x ^ { 2 } + 3 , \quad [ - 4,2 ]$$

Accepted Answer

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

Question 17

Find the limit algebraically.
-$$\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 9 } { x - 3 }$$

Accepted Answer

A)  Does not exist 
B)  3 
C)  1 
D)  6 
A)  Does not exist 
B)  3 
C)  1 
D)  6

Question 18

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.
-$$f ( x ) = 5 x - 1 \text { from } x = 1 \text { to } x = 4 ; n = 2$$

Accepted Answer

A)  $55.75$ 
B)  $25.75$ 
C)  $35.75$ 
D)  $45.75$ 
A)  $55.75$ 
B)  $25.75$ 
C)  $35.75$ 
D)  $45.75$

Question 19

Use the grid to graph the function. Find the limit, if it exists
-$$\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { r l } 
x + 1 & x < 0 \
4 x + 1 & x \geq 0
\end{array} \right.$$

Accepted Answer

A)  0 
B)  1 
C)  5 
D)  does not exist 
A)  0 
B)  1 
C)  5 
D)  does not exist

Question 20

Find the limit algebraically.
-$$\lim _ { x \rightarrow + } \frac { 3 x ^ { 2 } + 7 x - 2 } { 3 x ^ { 2 } - 4 x + 2 }$$

Accepted Answer

A)  $- \frac { 7 } { 4 }$ 
B)  0 
C)  8 
D)  does not exist 
A)  $- \frac { 7 } { 4 }$ 
B)  0 
C)  8 
D)  does not exist

Find the equation of the tangent line to the graph of f at the given point. - $f ( x ) = x ^ { 2 } + 5 x$ at $( 4,20 )$

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

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } \frac { 2 \sin x } { 4 x }$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = 4 \tan x$

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } \left( x ^ { 2 } - 5 \right)$

Find the one-sided limit. - $\lim _ { x \rightarrow - ^ { - } } ( 4 - 5 x )$

Find the limit as x approaches c of the average rate of change of the function from c to x. - $c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10$

Determine whether f is continuous at c. - $f ( x ) = \frac { 5 } { x ^ { 2 } - 2 x } ; \quad c = 0$

Use the TABLE feature of a graphing utility to find the limit. - $\lim _ { d \rightarrow 3 } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)$

Use the graph of y = g(x) to answer the question. $Use the graph of y = g(x) to answer the question. -Find \lim _ { x \rightarrow - 1 } g ( x ) .$ -Find $\lim _ { x \rightarrow - 1 } g ( x )$ .

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The volume $V$ of a right circular cylinder of height 2 and radius $r$ is $V ( r ) = 2 \pi r ^ { 2 }$ . Find the instantaneous rate of change of volume with respect to radius $r$ when $r = 7$ .

Choose the one alternative that best completes the statement or answers the question. -What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ represent?

Write the word or phrase that best completes each statement or answers the question. Find the derivative of the function at the given value of x using a graphing utility. If necessary, round to four decimal places. - $f ( x ) = 4 x \cos x ; x = \frac { \pi } { 2 }$

Find the limit algebraically. - $\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 9 } { x - 3 }$

Find the limit algebraically. - $\lim _ { x \rightarrow + } \frac { 3 x ^ { 2 } + 7 x - 2 } { 3 x ^ { 2 } - 4 x + 2 }$

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

Find the equation of the tangent line to the graph of f at the given point. - f(x)=x2+5xf ( x ) = x ^ { 2 } + 5 xf(x)=x2+5x at (4,20)( 4,20 )(4,20)

Find the numbers at which f is continuous. At which numbers is f discontinuous? - f(x)=−3cos⁡xf ( x ) = - 3 \cos xf(x)=−3cosx

Find the limit algebraically. - lim⁡x→02sin⁡x4x\lim _ { x \rightarrow 0 } \frac { 2 \sin x } { 4 x }limx→0​4x2sinx​

Find the numbers at which f is continuous. At which numbers is f discontinuous? - f(x)=4tan⁡xf ( x ) = 4 \tan xf(x)=4tanx

Find the limit algebraically. - lim⁡x→0(x2−5)\lim _ { x \rightarrow 0 } \left( x ^ { 2 } - 5 \right)limx→0​(x2−5)

Find the one-sided limit. - lim⁡x→−−(4−5x)\lim _ { x \rightarrow - ^ { - } } ( 4 - 5 x )limx→−−​(4−5x)

Find the limit as x approaches c of the average rate of change of the function from c to x. - c=9;f(x)=x3+10c = 9 ; \quad f ( x ) = \frac { x } { 3 } + 10c=9;f(x)=3x​+10

Choose the one alternative that best completes the statement or answers the question. -Provide a graph that illustrates the area represented by the integral. ∫23x2dx\int _ { 2 } ^ { 3 } x ^ { 2 } d x∫23​x2dx

Determine whether f is continuous at c. - f(x)=5x2−2x;c=0f ( x ) = \frac { 5 } { x ^ { 2 } - 2 x } ; \quad c = 0f(x)=x2−2x5​;c=0

Use the TABLE feature of a graphing utility to find the limit. - lim⁡d→3(d3−27d−3)\lim _ { d \rightarrow 3 } \left( \frac { d ^ { 3 } - 27 } { d - 3 } \right)limd→3​(d−3d3−27​)

Use the graph of y = g(x) to answer the question. -Find lim⁡x→−1g(x)\lim _ { x \rightarrow - 1 } g ( x )limx→−1​g(x) .

Choose the one alternative that best completes the statement or answers the question. -What area does the integral ∫ln⁡6ln⁡5exdx\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x∫ln6ln5​exdx represent?

Find the limit algebraically. - lim⁡x→3x2−9x−3\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 9 } { x - 3 }limx→3​x−3x2−9​

Use the grid to graph the function. Find the limit, if it exists - lim⁡x→0f(x),f(x)={x+1x<04x+1x≥0\lim _ { x \rightarrow 0 } f ( x ) , f ( x ) = \left\{ \begin{array} { r l } x + 1 & x < 0 \\4 x + 1 & x \geq 0\end{array} \right.limx→0​f(x),f(x)={x+14x+1​x<0x≥0​

Find the limit algebraically. - lim⁡x→+3x2+7x−23x2−4x+2\lim _ { x \rightarrow + } \frac { 3 x ^ { 2 } + 7 x - 2 } { 3 x ^ { 2 } - 4 x + 2 }limx→+​3x2−4x+23x2+7x−2​