Question 1

Find the one-sided limit.
-$$\lim _ { x \rightarrow 2 ^ { + } } \left( x ^ { 2 } - 3 x - 3 \right)$$

Accepted Answer

A)  13 
B)  $- 5$ 
C)  1 
D)  7 
A)  13 
B)  $- 5$ 
C)  1 
D)  7

Question 2

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-The function $\mathrm { V } ( \mathrm { r } ) = 4 \pi \mathrm { r } ^ { 2 }$ describes the volume of a right circular cylinder of height 4 feet and radius $\mathrm { r }$ feet. Find the instantaneous rate of change of the volume with respect to the radius when $r = 11$. Leave answer in terms of $\pi$

Accepted Answer

A)  $8 \pi$ cubic feet per feet 
B)  $44 \pi$ cubic feet per feet 
C)  $22 \pi$ cubic feet per feet 
D)  $88 \pi$ cubic feet per feet 
A)  $8 \pi$ cubic feet per feet 
B)  $44 \pi$ cubic feet per feet 
C)  $22 \pi$ cubic feet per feet 
D)  $88 \pi$ cubic feet per feet

Question 3

Use the TABLE feature of a graphing utility to find the limit.
-$$\lim _ { x \rightarrow - 0 } \frac { x ^ { 2 } } { \cos x }$$

Accepted Answer

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

Question 4

Choose the one alternative that best completes the statement or answers the question.
Find the slope of the tangent line to the graph at the given point.
-$$f ( x ) = x ^ { 2 } + 5 x \text { at } ( 4,20 )$$

Accepted Answer

A)  3 
B)  21 
C)  13 
D)  9 
A)  3 
B)  21 
C)  13 
D)  9

Question 5

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } ( \sqrt { x } - 2 )$$

Accepted Answer

A)  $- 2$ 
B)  2 
C)  0 
D)  does not exist 
A)  $- 2$ 
B)  2 
C)  0 
D)  does not exist

Question 6

Find the limit algebraically.
-$$\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }$$

Accepted Answer

A)  2 
B)  0 
C)  4 
D)  Does not exist 
A)  2 
B)  0 
C)  4 
D)  Does not exist

Question 7

Use the graph shown to determine if the limit exists. If it does, find its value.
-$\lim _{x \rightarrow 4} f(x)$

Accepted Answer

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

Question 8

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-A foul tip of a baseball is hit straight upward from a height of 4 feet with an initial velocity of 112 feet per second. The function $s ( t ) = - 16 t ^ { 2 } + 112 t + 4$ describes the ball's height above the ground, s(t), in feet, $t$ seconds after it was hit. The ball reaches its maximum height above the ground when the instantaneous speed reaches zero. After how many seconds does the ball reach its maximum height?

Accepted Answer

A)  112 
B)  $\frac { 3 } { 32 }$ 
C)  $\frac { 7 } { 2 }$ 
D)  7 
A)  112 
B)  $\frac { 3 } { 32 }$ 
C)  $\frac { 7 } { 2 }$ 
D)  7

Question 9

Find the limit algebraically.
-$$\lim _ { x \rightarrow 1 } \sqrt { 3 x - 2 }$$

Accepted Answer

A)  $- 1$ 
B)  1 
C)  $\sqrt { 2 }$ 
D)  does not exist 
A)  $- 1$ 
B)  1 
C)  $\sqrt { 2 }$ 
D)  does not exist

Question 10

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.
-$$f ( x ) = 2 x ^ { 2 } + x + 3 \text { from } x = 0 \text { to } x = 6 ; n = 6$$

Accepted Answer

A)  200 
B)  221 
C)  211 
D)  230 
A)  200 
B)  221 
C)  211 
D)  230

Question 11

Use the TABLE feature of a graphing utility to find the limit.
-$$\lim _ { h \rightarrow 3 } \left( \frac { h ^ { 2 } - 9 } { h ^ { 2 } + 3 h } \right)$$

Accepted Answer

A)  2 
B)  $- 2$ 
C)  0 
D)  does not exist 
A)  2 
B)  $- 2$ 
C)  0 
D)  does not exist

Question 12

Determine whether f is continuous at c.
-$$f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + x - 2 ; \quad c = 2$$

Accepted Answer

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

Question 13

Use the TABLE feature of a graphing utility to find the limit.
-$$\lim _ { x \rightarrow 0 } \frac { x + 2 } { 5 x + 2 }$$

Accepted Answer

A)  $\frac { 2 } { 5 }$ 
B)  0 
C)  1 
D)  does not exist 
A)  $\frac { 2 } { 5 }$ 
B)  0 
C)  1 
D)  does not exist

Question 14

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{aligned}
- 2 x + 3 , & x  1
\end{aligned} \right.$$

Accepted Answer

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

Question 15

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } - 6 x + 8 } { x - 2 }$$

Accepted Answer

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

Question 16

Find the limit as x approaches c of the average rate of change of the function from c to x.
-$$c = 4 ; \quad f ( x ) = \frac { 3 } { x }$$

Accepted Answer

A)  $= \frac { 3 } { 16 }$ 
B)  $- 12$ 
C)  $\frac { 3 } { 4 }$ 
D)  Does not exist 
A)  $= \frac { 3 } { 16 }$ 
B)  $- 12$ 
C)  $\frac { 3 } { 4 }$ 
D)  Does not exist

Question 17

Use the graph of y = g(x) to answer the question.  
-What is the domain of $g$ ?

Accepted Answer

A)  $\{ x \mid - 4 \leq x < 5 \}$ 
B)  $\{ x \mid - 4 \leq x < 4$ or $4 < x \leq 5 \}$ 
C)  $\{ x \mid - 4 < x < 5 \}$ 
D)  $\{ x \mid - 4 < x < - 1$ or $- 1 < x < 2$ or $2 < x \leq 5 \}$ 
A)  $\{ x \mid - 4 \leq x < 5 \}$ 
B)  $\{ x \mid - 4 \leq x < 4$ or $4 < x \leq 5 \}$ 
C)  $\{ x \mid - 4 < x < 5 \}$ 
D)  $\{ x \mid - 4 < x < - 1$ or $- 1 < x < 2$ or $2 < x \leq 5 \}$

Question 18

Determine whether f is continuous at c.
-$$f ( x ) = 2 x ^ { 4 } - 8 x ^ { 3 } + x - 5 ; \quad c = 8$$

Accepted Answer

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

Question 19

Use the graph of y = g(x) to answer the question.  
-Find the $\mathrm { y }$-intercept(s), if any, of $\mathrm { g }$.

Accepted Answer

A)  3 
B)  0 
C)  $- 1$ 
D)  $- \frac { 4 } { 3 }$ 
A)  3 
B)  0 
C)  $- 1$ 
D)  $- \frac { 4 } { 3 }$

Question 20

Find the limit algebraically.
-$$\lim _ { x \rightarrow 2 } ( 2 x + 7 )$$

Accepted Answer

A)  $- 18$ 
B)  9 
C)  3 
D)  does not exist 
A)  $- 18$ 
B)  9 
C)  3 
D)  does not exist

Find the one-sided limit. - $\lim _ { x \rightarrow 2 ^ { + } } \left( x ^ { 2 } - 3 x - 3 \right)$

Use the TABLE feature of a graphing utility to find the limit. - $\lim _ { x \rightarrow - 0 } \frac { x ^ { 2 } } { \cos x }$

Choose the one alternative that best completes the statement or answers the question. Find the slope of the tangent line to the graph at the given point. - $f ( x ) = x ^ { 2 } + 5 x \text { at } ( 4,20 )$

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } ( \sqrt { x } - 2 )$

Find the limit algebraically. - $\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }$

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _{x \rightarrow 4} f(x)$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _{x \rightarrow 4} f(x)$

Find the limit algebraically. - $\lim _ { x \rightarrow 1 } \sqrt { 3 x - 2 }$

Use the TABLE feature of a graphing utility to find the limit. - $\lim _ { h \rightarrow 3 } \left( \frac { h ^ { 2 } - 9 } { h ^ { 2 } + 3 h } \right)$

Determine whether f is continuous at c. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + x - 2 ; \quad c = 2$

Use the TABLE feature of a graphing utility to find the limit. - $\lim _ { x \rightarrow 0 } \frac { x + 2 } { 5 x + 2 }$

Determine whether f is continuous at c. - $f ( x ) = \left\{ \begin{aligned}- 2 x + 3 , & x < 1 \\1 , & x = 1 ; \quad c = 1 \\4 x - 1 , & x > 1\end{aligned} \right.$

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } - 6 x + 8 } { x - 2 }$

Find the limit as x approaches c of the average rate of change of the function from c to x. - $c = 4 ; \quad f ( x ) = \frac { 3 } { x }$

Use the graph of y = g(x) to answer the question. -What is the domain of $g$ ?

Determine whether f is continuous at c. - $f ( x ) = 2 x ^ { 4 } - 8 x ^ { 3 } + x - 5 ; \quad c = 8$

Use the graph of y = g(x) to answer the question. $Use the graph of y = g(x) to answer the question. -Find the \mathrm { y } -intercept(s), if any, of \mathrm { g } .$ -Find the $\mathrm { y }$ -intercept(s), if any, of $\mathrm { g }$ .

Find the limit algebraically. - $\lim _ { x \rightarrow 2 } ( 2 x + 7 )$

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 one-sided limit. - lim⁡x→2+(x2−3x−3)\lim _ { x \rightarrow 2 ^ { + } } \left( x ^ { 2 } - 3 x - 3 \right)limx→2+​(x2−3x−3)

Use the TABLE feature of a graphing utility to find the limit. - lim⁡x→−0x2cos⁡x\lim _ { x \rightarrow - 0 } \frac { x ^ { 2 } } { \cos x }limx→−0​cosxx2​

Choose the one alternative that best completes the statement or answers the question. Find the slope of the tangent line to the graph at the given point. - f(x)=x2+5x at (4,20)f ( x ) = x ^ { 2 } + 5 x \text { at } ( 4,20 )f(x)=x2+5x at (4,20)

Find the limit algebraically. - lim⁡x→0(x−2)\lim _ { x \rightarrow 0 } ( \sqrt { x } - 2 )limx→0​(x​−2)

Find the limit algebraically. - lim⁡x→1x4−1x−1\lim _ { x \rightarrow 1 } \frac { x ^ { 4 } - 1 } { x - 1 }limx→1​x−1x4−1​

Use the graph shown to determine if the limit exists. If it does, find its value. - lim⁡x→4f(x)\lim _{x \rightarrow 4} f(x)limx→4​f(x)

Find the limit algebraically. - lim⁡x→13x−2\lim _ { x \rightarrow 1 } \sqrt { 3 x - 2 }limx→1​3x−2​

Use the TABLE feature of a graphing utility to find the limit. - lim⁡h→3(h2−9h2+3h)\lim _ { h \rightarrow 3 } \left( \frac { h ^ { 2 } - 9 } { h ^ { 2 } + 3 h } \right)limh→3​(h2+3hh2−9​)

Determine whether f is continuous at c. - f(x)=3x4−7x3+x−2;c=2f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + x - 2 ; \quad c = 2f(x)=3x4−7x3+x−2;c=2

Use the TABLE feature of a graphing utility to find the limit. - lim⁡x→0x+25x+2\lim _ { x \rightarrow 0 } \frac { x + 2 } { 5 x + 2 }limx→0​5x+2x+2​

Determine whether f is continuous at c. - f(x)={−2x+3,x<11,x=1;c=14x−1,x>1f ( x ) = \left\{ \begin{aligned}- 2 x + 3 , & x < 1 \\1 , & x = 1 ; \quad c = 1 \\4 x - 1 , & x > 1\end{aligned} \right.f(x)=⎩⎨⎧​−2x+3,1,4x−1,​x<1x=1;c=1x>1​

Find the limit algebraically. - lim⁡x→0x3−6x+8x−2\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } - 6 x + 8 } { x - 2 }limx→0​x−2x3−6x+8​

Find the limit as x approaches c of the average rate of change of the function from c to x. - c=4;f(x)=3xc = 4 ; \quad f ( x ) = \frac { 3 } { x }c=4;f(x)=x3​

Use the graph of y = g(x) to answer the question. -What is the domain of ggg ?

Determine whether f is continuous at c. - f(x)=2x4−8x3+x−5;c=8f ( x ) = 2 x ^ { 4 } - 8 x ^ { 3 } + x - 5 ; \quad c = 8f(x)=2x4−8x3+x−5;c=8

Use the graph of y = g(x) to answer the question. -Find the y\mathrm { y }y -intercept(s), if any, of g\mathrm { g }g .

Find the limit algebraically. - lim⁡x→2(2x+7)\lim _ { x \rightarrow 2 } ( 2 x + 7 )limx→2​(2x+7)