Question 1

Find the limit algebraically.
-$$\lim _ { x \rightarrow } \left( 6 - 3 x ^ { 2 } \right)$$

Accepted Answer

A)  $- 48$ 
B)  $- 237$ 
C)  249 
D)  $- 21$ 
A)  $- 48$ 
B)  $- 237$ 
C)  249 
D)  $- 21$

Question 2

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.
-$$f ( x ) = - 4 x ^ { 2 } + 7 x \text { at } ( 5,65 )$$

Accepted Answer

A)  $- 13$ 
B)  33 
C)  $- 33$ 
D)  3 
A)  $- 13$ 
B)  33 
C)  $- 33$ 
D)  3

Question 3

Use the graph of y = g(x) to answer the question.  
-Find $f ( 2 )$

Accepted Answer

A)  1 
B)  2 
C)  $- \frac { 1 } { 2 }$ 
D)  3 
A)  1 
B)  2 
C)  $- \frac { 1 } { 2 }$ 
D)  3

Question 4

Determine whether f is continuous at c.
-$$f ( x ) = \frac { x - 2 } { x + 9 } ; c = - 9$$

Accepted Answer

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

Question 5

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

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.
-$$\lim _ { x \rightarrow } \frac { 2 x - 7 } { 4 x + 5 }$$

Accepted Answer

A)  $- \frac { 5 } { 9 }$ 
B)  $- \frac { 7 } { 5 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  does not exist 
A)  $- \frac { 5 } { 9 }$ 
B)  $- \frac { 7 } { 5 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  does not exist

Question 7

Determine whether f is continuous at c.
-$$f ( x ) = \frac { x - 7 } { x + 9 } ; c = 7$$

Accepted Answer

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

Question 8

Use the graph shown to determine if the limit exists. If it does, find its value.
-$\lim _{x \rightarrow 2} f(x)$

Accepted Answer

A)  0 
B)  1 
C)  2 
D)  does not exist 
A)  0 
B)  1 
C)  2 
D)  does not exist

Question 9

Find the limit as x approaches c of the average rate of change of the function from c to x.
-$$c = 3 ; \quad f ( x ) = 5 x + 3$$

Accepted Answer

A)  $- 5$ 
B)  3 
C)  5 
D)  $- 3$ 
A)  $- 5$ 
B)  3 
C)  5 
D)  $- 3$

Question 10

Determine whether f is continuous at c.
-$$f ( x ) = \frac { - 1 } { x ^ { 2 } + 8 x } ; \quad c = - 8$$

Accepted Answer

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

Question 11

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

Accepted Answer

A)  all real numbers 
B)  $\{ y \mid 2 \leq y \leq 4 \}$ 
C)  $\{ y \mid - 2 \leq y \leq 4 \}$ 
D)  $\{ y \mid - 2 \leq y \leq 5 \}$ 
A)  all real numbers 
B)  $\{ y \mid 2 \leq y \leq 4 \}$ 
C)  $\{ y \mid - 2 \leq y \leq 4 \}$ 
D)  $\{ y \mid - 2 \leq y \leq 5 \}$

Question 12

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.
-$$f ( x ) = x ^ { 2 } + 2 \text { from } x = 1 \text { to } x = 4 ; n = 6$$

Accepted Answer

A)  $24.875$ 
B)  $26.875$ 
C)  $30.875$ 
D)  $28.875$ 
A)  $24.875$ 
B)  $26.875$ 
C)  $30.875$ 
D)  $28.875$

Question 13

Find the limit algebraically.
-$$\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }$$

Accepted Answer

A)  Does not exist 
B)  5 
C)  0 
D)  $- 8$ 
A)  Does not exist 
B)  5 
C)  0 
D)  $- 8$

Question 14

Determine whether f is continuous at c.
-$$f ( x ) = \left\{ \begin{aligned}
x ^ { 2 } + 1 , & x < 0 ; \quad c = - 2 \
5 , & x \geq 0
\end{aligned} \right.$$

Accepted Answer

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

Question 15

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }$$

Accepted Answer

A)  continuous for all real numbers except $x = - 8 , x = - 3$ 
B)  continuous for all real numbers except $x = 8 , x = 3$ 
C)  continuous for all real numbers except $x = - 5 , x = 8$, and $x = 3$ 
D)  continuous for all real numbers except $x = 5 , x = - 8$, and $x = - 3$ 
A)  continuous for all real numbers except $x = - 8 , x = - 3$ 
B)  continuous for all real numbers except $x = 8 , x = 3$ 
C)  continuous for all real numbers except $x = - 5 , x = 8$, and $x = 3$ 
D)  continuous for all real numbers except $x = 5 , x = - 8$, and $x = - 3$

Question 16

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.
-$$f ( x ) = 2 x - 9 \text { at } ( 8,7 )$$

Accepted Answer

A)  9 
B)  $\frac { 1 } { 2 }$ 
C)  2 
D)  $- 9$ 
A)  9 
B)  $\frac { 1 } { 2 }$ 
C)  2 
D)  $- 9$

Question 17

Find the limit algebraically.
-$$\lim _ { x \rightarrow - } \frac { x ^ { 3 } + 5 x ^ { 2 } + 3 x - 9 } { x - 1 }$$

Accepted Answer

A)  $- 16$ 
B)  0 
C)  16 
D)  does not exist 
A)  $- 16$ 
B)  0 
C)  16 
D)  does not exist

Question 18

Determine whether f is continuous at c.
-$$f ( x ) = \frac { x ^ { 2 } - 25 } { x - 5 } ; \quad c = 0$$

Accepted Answer

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

Question 19

Find the limit algebraically.
-$$\lim _ { x \rightarrow 1 } - 6$$

Accepted Answer

A)  $- 6$ 
B)  1 
C)  0 
D)  6 
A)  $- 6$ 
B)  1 
C)  0 
D)  6

Question 20

Find the numbers at which f is continuous. At which numbers is f discontinuous?
-$$f ( x ) = \left\{ \begin{aligned}
x - 5 & \text { if } x \leq 5 \
2 x - 10 & \text { if } x > 5
\end{aligned} \right.$$

Accepted Answer

A)  continuous for all real numbers except $x = - 5 , x = 5$ 
B)  continuous for all real numbers except $x = 5$ 
C)  continuous for all real numbers 
D)  continuous for all real numbers except $x = 0$ 
A)  continuous for all real numbers except $x = - 5 , x = 5$ 
B)  continuous for all real numbers except $x = 5$ 
C)  continuous for all real numbers 
D)  continuous for all real numbers except $x = 0$

Find the limit algebraically. - $\lim _ { x \rightarrow } \left( 6 - 3 x ^ { 2 } \right)$

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. - $f ( x ) = - 4 x ^ { 2 } + 7 x \text { at } ( 5,65 )$

Use the graph of y = g(x) to answer the question. -Find $f ( 2 )$

Determine whether f is continuous at c. - $f ( x ) = \frac { x - 2 } { x + 9 } ; c = - 9$

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

Find the limit algebraically. - $\lim _ { x \rightarrow } \frac { 2 x - 7 } { 4 x + 5 }$

Determine whether f is continuous at c. - $f ( x ) = \frac { x - 7 } { x + 9 } ; c = 7$

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _{x \rightarrow 2} f(x)$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _{x \rightarrow 2} f(x)$

Find the limit as x approaches c of the average rate of change of the function from c to x. - $c = 3 ; \quad f ( x ) = 5 x + 3$

Determine whether f is continuous at c. - $f ( x ) = \frac { - 1 } { x ^ { 2 } + 8 x } ; \quad c = - 8$

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

Find the limit algebraically. - $\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }$

Determine whether f is continuous at c. - $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } + 1 , & x < 0 ; \quad c = - 2 \\5 , & x \geq 0\end{aligned} \right.$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }$

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. - $f ( x ) = 2 x - 9 \text { at } ( 8,7 )$

Find the limit algebraically. - $\lim _ { x \rightarrow - } \frac { x ^ { 3 } + 5 x ^ { 2 } + 3 x - 9 } { x - 1 }$

Determine whether f is continuous at c. - $f ( x ) = \frac { x ^ { 2 } - 25 } { x - 5 } ; \quad c = 0$

Find the limit algebraically. - $\lim _ { x \rightarrow 1 } - 6$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \left\{ \begin{aligned}x - 5 & \text { if } x \leq 5 \\2 x - 10 & \text { if } x > 5\end{aligned} \right.$

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

Find the limit algebraically. - lim⁡x→(6−3x2)\lim _ { x \rightarrow } \left( 6 - 3 x ^ { 2 } \right)limx→​(6−3x2)

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)=−4x2+7x at (5,65)f ( x ) = - 4 x ^ { 2 } + 7 x \text { at } ( 5,65 )f(x)=−4x2+7x at (5,65)

Use the graph of y = g(x) to answer the question. -Find f(2)f ( 2 )f(2)

Determine whether f is continuous at c. - f(x)=x−2x+9;c=−9f ( x ) = \frac { x - 2 } { x + 9 } ; c = - 9f(x)=x+9x−2​;c=−9

Find the one-sided limit. - lim⁡x→θ+(2cos⁡x)\lim _ { x \rightarrow \theta ^ { + } } ( 2 \cos x )limx→θ+​(2cosx)

Find the limit algebraically. - lim⁡x→2x−74x+5\lim _ { x \rightarrow } \frac { 2 x - 7 } { 4 x + 5 }limx→​4x+52x−7​

Determine whether f is continuous at c. - f(x)=x−7x+9;c=7f ( x ) = \frac { x - 7 } { x + 9 } ; c = 7f(x)=x+9x−7​;c=7

Use the graph shown to determine if the limit exists. If it does, find its value. - lim⁡x→2f(x)\lim _{x \rightarrow 2} f(x)limx→2​f(x)

Find the limit as x approaches c of the average rate of change of the function from c to x. - c=3;f(x)=5x+3c = 3 ; \quad f ( x ) = 5 x + 3c=3;f(x)=5x+3

Determine whether f is continuous at c. - f(x)=−1x2+8x;c=−8f ( x ) = \frac { - 1 } { x ^ { 2 } + 8 x } ; \quad c = - 8f(x)=x2+8x−1​;c=−8

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

Find the limit algebraically. - lim⁡x→3x2−2x−15x+3\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }limx→3​x+3x2−2x−15​

Determine whether f is continuous at c. - f(x)={x2+1,x<0;c=−25,x≥0f ( x ) = \left\{ \begin{aligned}x ^ { 2 } + 1 , & x < 0 ; \quad c = - 2 \\5 , & x \geq 0\end{aligned} \right.f(x)={x2+1,5,​x<0;c=−2x≥0​

Find the numbers at which f is continuous. At which numbers is f discontinuous? - f(x)=x+5x2−11x+24f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }f(x)=x2−11x+24x+5​

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)=2x−9 at (8,7)f ( x ) = 2 x - 9 \text { at } ( 8,7 )f(x)=2x−9 at (8,7)

Find the limit algebraically. - lim⁡x→−x3+5x2+3x−9x−1\lim _ { x \rightarrow - } \frac { x ^ { 3 } + 5 x ^ { 2 } + 3 x - 9 } { x - 1 }limx→−​x−1x3+5x2+3x−9​

Determine whether f is continuous at c. - f(x)=x2−25x−5;c=0f ( x ) = \frac { x ^ { 2 } - 25 } { x - 5 } ; \quad c = 0f(x)=x−5x2−25​;c=0

Find the limit algebraically. - lim⁡x→1−6\lim _ { x \rightarrow 1 } - 6limx→1​−6

Find the numbers at which f is continuous. At which numbers is f discontinuous? - f(x)={x−5 if x≤52x−10 if x>5f ( x ) = \left\{ \begin{aligned}x - 5 & \text { if } x \leq 5 \\2 x - 10 & \text { if } x > 5\end{aligned} \right.f(x)={x−52x−10​ if x≤5 if x>5​

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

Find the limit algebraically. - $\lim _ { x \rightarrow } \left( 6 - 3 x ^ { 2 } \right)$

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. - $f ( x ) = - 4 x ^ { 2 } + 7 x \text { at } ( 5,65 )$

Use the graph of y = g(x) to answer the question. -Find $f ( 2 )$

Determine whether f is continuous at c. - $f ( x ) = \frac { x - 2 } { x + 9 } ; c = - 9$

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

Find the limit algebraically. - $\lim _ { x \rightarrow } \frac { 2 x - 7 } { 4 x + 5 }$

Determine whether f is continuous at c. - $f ( x ) = \frac { x - 7 } { x + 9 } ; c = 7$

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _{x \rightarrow 2} f(x)$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _{x \rightarrow 2} f(x)$

Find the limit as x approaches c of the average rate of change of the function from c to x. - $c = 3 ; \quad f ( x ) = 5 x + 3$

Determine whether f is continuous at c. - $f ( x ) = \frac { - 1 } { x ^ { 2 } + 8 x } ; \quad c = - 8$

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

Find the limit algebraically. - $\lim _ { x \rightarrow 3 } \frac { x ^ { 2 } - 2 x - 15 } { x + 3 }$

Determine whether f is continuous at c. - $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } + 1 , & x < 0 ; \quad c = - 2 \\5 , & x \geq 0\end{aligned} \right.$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \frac { x + 5 } { x ^ { 2 } - 11 x + 24 }$

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. - $f ( x ) = 2 x - 9 \text { at } ( 8,7 )$

Find the limit algebraically. - $\lim _ { x \rightarrow - } \frac { x ^ { 3 } + 5 x ^ { 2 } + 3 x - 9 } { x - 1 }$

Determine whether f is continuous at c. - $f ( x ) = \frac { x ^ { 2 } - 25 } { x - 5 } ; \quad c = 0$

Find the limit algebraically. - $\lim _ { x \rightarrow 1 } - 6$

Find the numbers at which f is continuous. At which numbers is f discontinuous? - $f ( x ) = \left\{ \begin{aligned}x - 5 & \text { if } x \leq 5 \\2 x - 10 & \text { if } x > 5\end{aligned} \right.$