Question 1

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

Question 2

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 3

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.
-$$f ( x ) = 2 x ^ { 3 } - 1 \text { from } x = 1 \text { to } x = 6 ; n = 5$$

Accepted Answer

A)  850 
B)  825 
C)  875 
D)  800 
A)  850 
B)  825 
C)  875 
D)  800

Question 4

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

Accepted Answer

A)  3 
B)  4 
C)  0 
D)  -1 
A)  3 
B)  4 
C)  0 
D)  -1

Question 5

Solve the problem.
-What area does the integral $$\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$$ dx represent?

Accepted Answer

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

Question 6

Find the limit algebraically.
-$$\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }$$

Accepted Answer

A)  0 
B)  -1 
C)  5 
D)  Does not exist 
A)  0 
B)  -1 
C)  5 
D)  Does not exist

Question 7

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 Find the derivative of the function at...

Question 8

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 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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 12

Solve the problem.
-The function f $$f ( x ) = x ^ { 3 }$$ describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. Find the instantaneous rate of change of the volume with respect to x when x = 4 inches.

Accepted Answer

A)  12 cubic inches per inch 
B)  49.21 cubic inches per inch 
C)  48 cubic inches per inch 
D)  192 cubic inches per inch 
A)  12 cubic inches per inch 
B)  49.21 cubic inches per inch 
C)  48 cubic inches per inch 
D)  192 cubic inches per inch

Question 13

Use the graph shown to determine if the limit exists. If it does, find its value.
-$$\lim _ { x \rightarrow 1 } f ( x )$$

Accepted Answer

A)  1 
B)  3 
C)  0 
D)  does not exist 
A)  1 
B)  3 
C)  0 
D)  does not exist

Question 14

Solve the problem.
-$f ( x ) = \sqrt [ 3 ] { x }$ is defined on the interval 0, 6 .
(a) Approximate the area A under the graph of f by partitioning 0, 6 into three subintervals of equal length and
choose u as the left endpoint of each subinterval.
(b) Approximate the area A under the graph of f by partitioning 0, 6 into three subintervals of equal length and
choose u as the right endpoint of each subinterval.
(c) Express the area A as an integral.
(d) Use a graphing utility to approximate this integral to three decimal places.

Accepted Answer

(a) 5.695

Question 15

Solve the problem.
-The funct $$V ( r ) = 4 \pi r ^ { 2 }$$ describes the volume of a right circular cylinder of height 4 feet and radius r feet. Find the instantaneous rate of change of the volume with respect to the radius when r = 11. Leave answer in terms of $$\pi$$ . A) $8 \pi$ cubic feet per feet

Accepted Answer

B)  $44 \pi$ cubic feet per feet 
C)  $22 \pi$ cubic feet per feet 
D)  $88 \pi$ 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 16

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 17

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 18

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

Accepted Answer

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

Question 19

Find the derivative of the function at the given value of x.
-$$f ( x ) = x ^ { 2 } + 9 x + 9 ; x = 8$$

Accepted Answer

A)  9 
B)  11 
C)  25 
D)  16 
A)  9 
B)  11 
C)  25 
D)  16

Question 20

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

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

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

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. - $f ( x ) = 2 x ^ { 3 } - 1 \text { from } x = 1 \text { to } x = 6 ; n = 5$

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

Solve the problem. -What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ dx represent?

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }$

Find the derivative of the function at the given value of x using a graphing utility. If necessary, round to four decimal places. - $f ( x ) = 4 x \cos x ; x = \frac { \pi } { 2 }$

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

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

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

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

Solve the problem. -The function f $f ( x ) = x ^ { 3 }$ describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. Find the instantaneous rate of change of the volume with respect to x when x = 4 inches.

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 1 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 1 } f ( x )$

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

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

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

Find the derivative of the function at the given value of x. - $f ( x ) = x ^ { 2 } + 9 x + 9 ; x = 8$

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

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

Review

Filters

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

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

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

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

Solve the problem. -What area does the integral ∫ln⁡6ln⁡5exdx\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x∫ln6ln5​exdx dx represent?

Find the limit algebraically. - lim⁡x→0x3+12x2−5x5x\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }limx→0​5xx3+12x2−5x​

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)=4xcos⁡x;x=π2f ( x ) = 4 x \cos x ; x = \frac { \pi } { 2 }f(x)=4xcosx;x=2π​

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

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 ; c = - 2 \\5 , & x \geq 0\end{aligned} \right.f(x)={x2+1,5,​x<0;c=−2x≥0​

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

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

Solve the problem. -The function f f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. Find the instantaneous rate of change of the volume with respect to x when x = 4 inches.

Use the graph shown to determine if the limit exists. If it does, find its value. - lim⁡x→1f(x)\lim _ { x \rightarrow 1 } f ( x )limx→1​f(x)

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​

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

Find the derivative of the function at the given value of x. - f(x)=x2+9x+9;x=8f ( x ) = x ^ { 2 } + 9 x + 9 ; x = 8f(x)=x2+9x+9;x=8

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

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

Review

Filters

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

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

Solve the problem. -What area does the integral $\int _ { \ln 6 } ^ { \ln 5 } e ^ { x } d x$ dx represent?

Find the limit algebraically. - $\lim _ { x \rightarrow 0 } \frac { x ^ { 3 } + 12 x ^ { 2 } - 5 x } { 5 x }$

Find the derivative of the function at the given value of x using a graphing utility. If necessary, round to four decimal places. - $f ( x ) = 4 x \cos x ; x = \frac { \pi } { 2 }$

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

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

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

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

Solve the problem. -The function f $f ( x ) = x ^ { 3 }$ describes the volume of a cube, f(x), in cubic inches, whose length, width, and height each measure x inches. Find the instantaneous rate of change of the volume with respect to x when x = 4 inches.

Use the graph shown to determine if the limit exists. If it does, find its value. - $\lim _ { x \rightarrow 1 } f ( x )$ $Use the graph shown to determine if the limit exists. If it does, find its value. - \lim _ { x \rightarrow 1 } f ( x )$

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

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

Find the derivative of the function at the given value of x. - $f ( x ) = x ^ { 2 } + 9 x + 9 ; x = 8$

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