Question 1

Find the slope and y-intercept (if they exist)of the line 8y = 7x.

Accepted Answer

A) Slope is 7 and y-intercept is 8. 
B) Slope is $\frac { 8 } { 7 }$ and y-intercept is 0. 
C) Slope is $\frac { 7 } { 8 }$ and y-intercept is 0. 
D) Slope is 7 and y-intercept is 0. 
A) Slope is 7 and y-intercept is 8. 
B) Slope is $\frac { 8 } { 7 }$ and y-intercept is 0. 
C) Slope is $\frac { 7 } { 8 }$ and y-intercept is 0. 
D) Slope is 7 and y-intercept is 0. C

Question 2

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

Accepted Answer

A) 3 
B) Does not exist 
C) -1 
D) 7 
A) 3 
B) Does not exist 
C) -1 
D) 7 D

Question 3

Two car rental agencies are competing.One agency rents cars for 50 dollars per day and 35 cents a mile; the other agency rents cars for 35 dollars per day and 45 cents a mile.For a 10 day trip,how many miles must you travel to have the total cost be the same with each agency? Round to the nearest whole mile ,if necessary.

Accepted Answer

A) 43 miles 
B) 1,500 miles 
C) 33 miles 
D) 150 miles 
A) 43 miles 
B) 1,500 miles 
C) 33 miles 
D) 150 miles B

Question 4

Each unit of a certain commodity costs p = 47x + 12 cents when x units of the commodity are produced.If all units are sold at this price,express the revenue derived from the sales as a function of x.

Accepted Answer

A) 46x + 12 cents 
B)  $47 x ^ { 2 } + 12$ cents 
C) 48x + 12 cents 
D) x(47x + 12)cents 
A) 46x + 12 cents 
B)  $47 x ^ { 2 } + 12$ cents 
C) 48x + 12 cents 
D) x(47x + 12)cents

Question 5

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$

Accepted Answer

A)    
B)    
C)    
D)   
(Tick marks are spaced one unit apart.) 
A)    
B)    
C)    
D)   
(Tick marks are spaced one unit apart.)

Question 6

Find the distance between the given points. (-2,6)and (3,7)

Accepted Answer

A) D = 6 
B) D = 26 
C)  $D = \sqrt { 26 }$ 
D)  $D = \sqrt { 6 }$ 
A) D = 6 
B) D = 26 
C)  $D = \sqrt { 26 }$ 
D)  $D = \sqrt { 6 }$

Question 7

An efficiency consultant determines that when new workers are hired to wait tables at an upscale restaurant,the average number of tables they can wait on in a 6 hour shift is given by $N ( x ) = \frac { \sqrt { 5.3 x ^ { 2 } + 50 x + 14 } } { 0.1 x + 0.8 }$ where x is the number of shifts they've worked since being hired.What happens to an average waiter's productivity in the long run (as $x \rightarrow \infty$ )?

Accepted Answer

A) It approaches 53 tables per shift. 
B) It increases without bound. 
C) It approaches 23 tables per shift. 
D) It approaches 14 tables per shift. 
A) It approaches 53 tables per shift. 
B) It increases without bound. 
C) It approaches 23 tables per shift. 
D) It approaches 14 tables per shift.

Question 8

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

Accepted Answer

A) Does not exist 
B) 6 
C)  $\frac { 3 } { 2 }$ 
D) 3 
A) Does not exist 
B) 6 
C)  $\frac { 3 } { 2 }$ 
D) 3

Question 9

The cost of renting a backhoe at one distributor is $325,plus $35 per day.Write a linear function C(x)that describes the cost of renting the backhoe for x days,then use your function to find how much it would cost to rent it for 12 days.

Accepted Answer

A)  $C ( x ) = 35 x + 313 ; \quad \$ 733$ 
B)  $C ( x ) = 325 x + 35 ; \quad \$ 3,935$ 
C)  $C ( x ) = 12 ( 325 + 35 x ) ; \quad \$ 8,940$ 
D)  $C ( x ) = 325 + 35 x ; \quad \$ 745$ 
A)  $C ( x ) = 35 x + 313 ; \quad \$ 733$ 
B)  $C ( x ) = 325 x + 35 ; \quad \$ 3,935$ 
C)  $C ( x ) = 12 ( 325 + 35 x ) ; \quad \$ 8,940$ 
D)  $C ( x ) = 325 + 35 x ; \quad \$ 745$

Question 10

Compute the indicated value of the given function. $f ( t ) = \left\{ \begin{aligned}
- 2 t + 8 & \text { if } t < - 1 \
t ^ { 2 } + 9 & \text { if } t \geq - 1
\end{aligned} \right.$ ; f (-3)

Accepted Answer

A) 18 
B) 0 
C) 2 
D) 14 
A) 18 
B) 0 
C) 2 
D) 14

Question 11

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$

Accepted Answer

A)  $\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 9 } { x ( x + h ) }$ 
B)  $\frac { f ( x + h ) - f ( x ) } { h } = \frac { 9 } { x + h }$ 
C)  $\frac { f ( x + h ) - f ( x ) } { h }$ = 9 
D)  $\frac { f ( x + h ) - f ( x ) } { h }$ = 1 
A)  $\frac { f ( x + h ) - f ( x ) } { h } = - \frac { 9 } { x ( x + h ) }$ 
B)  $\frac { f ( x + h ) - f ( x ) } { h } = \frac { 9 } { x + h }$ 
C)  $\frac { f ( x + h ) - f ( x ) } { h }$ = 9 
D)  $\frac { f ( x + h ) - f ( x ) } { h }$ = 1

Question 12

List all values of x for which f (x)is not continuous. $f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$ .

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B) -1 
C) None 
D) 0 and -1 
A)  $- \frac { 1 } { 2 }$ 
B) -1 
C) None 
D) 0 and -1

Question 13

Plot the given point in a rectangular coordinate system. (1,-5)

Accepted Answer

A)    (Each gridline represents one unit.) 
B)    (Each gridline represents one unit.) 
C)    (Each gridline represents one unit.) 
D)    (Each gridline represents one unit.) 
A)    (Each gridline represents one unit.) 
B)    (Each gridline represents one unit.) 
C)    (Each gridline represents one unit.) 
D)    (Each gridline represents one unit.)

Question 14

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is +$\infty$ or -$\infty$. f (x)= (5 - 9x)(x - 2)

Accepted Answer

A) -$\infty$، - $\infty$ 
B) -$\infty$، 0 
C) +$\infty$، +$\infty$ 
D) +$\infty$، 0 
A) -$\infty$، - $\infty$ 
B) -$\infty$، 0 
C) +$\infty$، +$\infty$ 
D) +$\infty$، 0

Question 15

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is +$\infty$ or -$\infty$. $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) 2 
D) -2 
A)  $- \frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 4 }$ 
C) 2 
D) -2

Question 16

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is +$\infty$ or -$\infty$. $f ( x ) = \frac { 4 - 2 x ^ { 3 } } { 6 x ^ { 3 } - 6 x + 1 }$

Accepted Answer

A) +$\infty$،-$\infty$ 
B) -$\infty$، +$\infty$ 
C)  $- \frac { 1 } { 3 }$ , $- \frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 }$ , $\frac { 1 } { 3 }$ 
A) +$\infty$،-$\infty$ 
B) -$\infty$، +$\infty$ 
C)  $- \frac { 1 } { 3 }$ , $- \frac { 1 } { 3 }$ 
D)  $- \frac { 1 } { 3 }$ , $\frac { 1 } { 3 }$

Question 17

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is +$\infty$ or -$\infty$. $\lim _ { x \rightarrow 2 ^ { - } } f ( x )$ where $f ( x ) = \left\{ \begin{aligned}
x + 5 & \text { if } x < 2 \
x ^ { 2 } & \text { if } x \geq 2
\end{aligned} \right.$

Accepted Answer

A) There is none 
B) 7 
C) 0 
D) 4 
A) There is none 
B) 7 
C) 0 
D) 4

Question 18

Find the indicated composite function. f (x + 6)where $f ( x ) = \frac { 1 } { x }$

Accepted Answer

A) f (x + 6)= $x + 6 + \frac { 1 } { x }$ 
B) f (x + 6)= $\frac { 1 } { x + 6 }$ 
C) f (x + 6)= $1 + \frac { 3 } { x }$ 
D) f (x + 6)= $\frac { 1 } { x } + 6$ 
A) f (x + 6)= $x + 6 + \frac { 1 } { x }$ 
B) f (x + 6)= $\frac { 1 } { x + 6 }$ 
C) f (x + 6)= $1 + \frac { 3 } { x }$ 
D) f (x + 6)= $\frac { 1 } { x } + 6$

Question 19

A closed box with a square base is to have a volume of 10 cubic meters.The material for the top and bottom of the box costs $5 per square meter,and the material for the sides costs $1 per square meter.Express the construction cost of the box as a function of the length of its base,x.

Accepted Answer

A)  $C ( x ) = 10 x ^ { 2 } + \frac { 40 } { x }$ dollars 
B)  $C ( x ) = x ^ { 2 } + 40 x + 2$ dollars 
C)  $C ( x ) = 2 x ^ { 2 } + \frac { 2 } { x } + 10$ dollars 
D)  $C ( x ) = 2 x ^ { 2 } + \frac { 10 } { x }$ dollars 
A)  $C ( x ) = 10 x ^ { 2 } + \frac { 40 } { x }$ dollars 
B)  $C ( x ) = x ^ { 2 } + 40 x + 2$ dollars 
C)  $C ( x ) = 2 x ^ { 2 } + \frac { 2 } { x } + 10$ dollars 
D)  $C ( x ) = 2 x ^ { 2 } + \frac { 10 } { x }$ dollars

Question 20

Find the points of intersection (if any)of the given pair of curves. $y = x ^ { 2 }$ and y = 3x - 2.

Accepted Answer

A) There are no points of intersection. 
B) (2,4) 
C) (1,1),(2,4) 
D) (0,0) 
A) There are no points of intersection. 
B) (2,4) 
C) (1,1),(2,4) 
D) (0,0)

Find the slope and y-intercept (if they exist)of the line 8y = 7x.

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

Each unit of a certain commodity costs p = 47x + 12 cents when x units of the commodity are produced.If all units are sold at this price,express the revenue derived from the sales as a function of x.

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$

Find the distance between the given points. (-2,6)and (3,7)

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

The cost of renting a backhoe at one distributor is $325,plus $35 per day.Write a linear function C(x)that describes the cost of renting the backhoe for x days,then use your function to find how much it would cost to rent it for 12 days.

Compute the indicated value of the given function. $f ( t ) = \left\{ \begin{aligned}- 2 t + 8 & \text { if } t < - 1 \\t ^ { 2 } + 9 & \text { if } t \geq - 1\end{aligned} \right.$ ; f (-3)

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$

List all values of x for which f (x)is not continuous. $f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$ .

Plot the given point in a rectangular coordinate system. (1,-5)

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . f (x)= (5 - 9x)(x - 2)

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . $f ( x ) = \frac { 4 - 2 x ^ { 3 } } { 6 x ^ { 3 } - 6 x + 1 }$

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 2 ^ { - } } f ( x )$ where $f ( x ) = \left\{ \begin{aligned}x + 5 & \text { if } x < 2 \\x ^ { 2 } & \text { if } x \geq 2\end{aligned} \right.$

Find the indicated composite function. f (x + 6)where $f ( x ) = \frac { 1 } { x }$

A closed box with a square base is to have a volume of 10 cubic meters.The material for the top and bottom of the box costs $5 per square meter,and the material for the sides costs $1 per square meter.Express the construction cost of the box as a function of the length of its base,x.

Find the points of intersection (if any)of the given pair of curves. $y = x ^ { 2 }$ and y = 3x - 2.

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Exam 1: Functions,graphs,and Limits

Find the slope and y-intercept (if they exist)of the line 8y = 7x.

Find the indicated limit if it exists. lim⁡x→3(x+4)\lim _ { x \rightarrow 3 } ( x + 4 )limx→3​(x+4)

Each unit of a certain commodity costs p = 47x + 12 cents when x units of the commodity are produced.If all units are sold at this price,express the revenue derived from the sales as a function of x.

Sketch the graph of the given function. f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2

Find the distance between the given points. (-2,6)and (3,7)

Find the indicated limit if it exists. lim⁡x→1x2+3x+2x2−1\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }limx→1​x2−1x2+3x+2​

The cost of renting a backhoe at one distributor is $325,plus $35 per day.Write a linear function C(x)that describes the cost of renting the backhoe for x days,then use your function to find how much it would cost to rent it for 12 days.

Compute the indicated value of the given function. f(t)={−2t+8 if t<−1t2+9 if t≥−1f ( t ) = \left\{ \begin{aligned}- 2 t + 8 & \text { if } t < - 1 \\t ^ { 2 } + 9 & \text { if } t \geq - 1\end{aligned} \right.f(t)={−2t+8t2+9​ if t<−1 if t≥−1​ ; f (-3)

Find the difference quotient, f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ . f(x)=9xf ( x ) = \frac { 9 } { x }f(x)=x9​

List all values of x for which f (x)is not continuous. f(x)=2x+1x2+xf ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }f(x)=x2+x2x+1​ .

Plot the given point in a rectangular coordinate system. (1,-5)

Find lim⁡x→+∞f(x)\lim _ { x \rightarrow + \infty } f ( x )limx→+∞​f(x) and lim⁡x→−∞f(x)\lim _ { x \rightarrow - \infty } f ( x )limx→−∞​f(x) .If the limiting value is infinite indicate whether it is + ∞\infty∞ or - ∞\infty∞ . f (x)= (5 - 9x)(x - 2)

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is + ∞\infty∞ or - ∞\infty∞ . lim⁡x→4−x−2x−4\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }limx→4−​x−4x​−2​

Find the indicated composite function. f (x + 6)where f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​

A closed box with a square base is to have a volume of 10 cubic meters.The material for the top and bottom of the box costs $5 per square meter,and the material for the sides costs $1 per square meter.Express the construction cost of the box as a function of the length of its base,x.

Find the points of intersection (if any)of the given pair of curves. y=x2y = x ^ { 2 }y=x2 and y = 3x - 2.

Differentiation: Basic Concepts

Additional Applications of the Derivative

Exponential and Logarithmic Functions

Itegration

Additional Topics in Integration

Calculus of Several Variables

Differential Equations

Infinite Series and Taylor Series Approximations

Probability and Calculus

Trigonometric Functions

Calculus Practice Questions

Mathematical Problem Set: Calculus, Algebra, and Optimization

Filters

Find the indicated limit if it exists. $\lim _ { x \rightarrow 3 } ( x + 4 )$

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

Compute the indicated value of the given function. $f ( t ) = \left\{ \begin{aligned}- 2 t + 8 & \text { if } t < - 1 \\t ^ { 2 } + 9 & \text { if } t \geq - 1\end{aligned} \right.$ ; f (-3)

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$

List all values of x for which f (x)is not continuous. $f ( x ) = \frac { 2 x + 1 } { x ^ { 2 } + x }$ .

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ .If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . f (x)= (5 - 9x)(x - 2)

Find the indicated one-sided limit.If the limiting value is infinite,indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 4 ^ { - } } \frac { \sqrt { x } - 2 } { x - 4 }$

Find the indicated composite function. f (x + 6)where $f ( x ) = \frac { 1 } { x }$

Find the points of intersection (if any)of the given pair of curves. $y = x ^ { 2 }$ and y = 3x - 2.