Question 1

Write the general form of the equation of the circle with center   and solution point

Accepted Answer

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

Question 2

​State the signs of   and   on the interval (0,2). ​
​   ​

Accepted Answer

A) f ' 0 C) f ' > 0 f '' 0 f '' > 0 E) f ' < 0 f '' < 0 A) f ' 0 C) f ' > 0 f '' 0 f '' > 0 E) f ' < 0 f '' < 0

Question 3

​Use the given information to find   of the function   ​   ,   ,   and   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 4

​The profit (in dollars)from selling x units of calculus textbooks is given by   Find the marginal profit when   Round your answer to two decimal places. ​

Accepted Answer

A)  ​$35.00 
B)  ​$20.00 
C)  ​$5.00 
D)  ​$-125.00 
E)  ​$-130.05 
A)  ​$35.00 
B)  ​$20.00 
C)  ​$5.00 
D)  ​$-125.00 
E)  ​$-130.05

Question 5

​For the function   ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. ​
​

Accepted Answer

A)  ​2 
B)  ​0.5 
C)  ​1.5 
D)  ​3 
E)  ​1 
A)  ​2 
B)  ​0.5 
C)  ​1.5 
D)  ​3 
E)  ​1

Question 6

Use the properties of exponents to simplify the expression   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 7

​Find the point on the graph of   that is closest to the point (8,0.5).Round your answer to two decimal places. ​

Accepted Answer

A)  ​(1.59, 2.53) 
B)  ​(2, 4) 
C)  ​(2.52, 6.35) 
D)  ​(1.39, 1.93) 
E)  ​(1.26,1.59) 
A)  ​(1.59, 2.53) 
B)  ​(2, 4) 
C)  ​(2.52, 6.35) 
D)  ​(1.39, 1.93) 
E)  ​(1.26,1.59)

Question 8

​Find all relative maxima of the given function. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative maxima 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​no relative maxima

Question 9

Sketch the graph of the function   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 10

​Find the relative minima,and use a graphing utility to check your results. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​0 
E)  ​does not exist 
A)  ​   
B)  ​   
C)  ​   
D)  ​0 
E)  ​does not exist

Question 11

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​   ​

Accepted Answer

A)  ​-2.993 
B)  ​-0.100 
C)  ​2.182 
D)  ​-1.091 
E)  ​5.986 
A)  ​-2.993 
B)  ​-0.100 
C)  ​2.182 
D)  ​-1.091 
E)  ​5.986

Question 12

​Find the slope m and y-intercept b of the line whose equation is given below. ​   ​

Accepted Answer

A)  ​   ,   
B)  ​​   ,   
C)  ​​​   ,   
D)  ​   ,   
E)  ​   ,   
A)  ​   ,   
B)  ​​   ,   
C)  ​​​   ,   
D)  ​   ,   
E)  ​   ,

Question 13

​Solve the following equation for x accurate to three decimal places. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 14

Suppose that the annual rate of inflation averages 4% over the next 10 years.With this rate of inflation,the approximate cost C of goods or services during any year in that decade will be given by   ,   where t is time in years and P is the present cost.If the price of an oil change for your car is presently $25.95,estimate the price 10 years from now.Round your answer to two decimal places.

Accepted Answer

A)  $39.95 
B)  $40.41 
C)  $41.95 
D)  $43.41 
E)  $38.41 
A)  $39.95 
B)  $40.41 
C)  $41.95 
D)  $43.41 
E)  $38.41

Question 15

​Sketch the graph of the equation given below.Use intercepts,extrema,and asymptotes as sketching aids. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 16

​Determine the open intervals on which the graph of   is concave downward or concave upward.

Accepted Answer

A)  ​concave upward on   ; concave downward on   
B)  ​concave downward on   
C)  ​concave upward on   
D)  ​concave downward on   ; ​concave upward   
E)  ​​concave upward on   ; concave downward on   
A)  ​concave upward on   ; concave downward on   
B)  ​concave downward on   
C)  ​concave upward on   
D)  ​concave downward on   ; ​concave upward   
E)  ​​concave upward on   ; concave downward on

Question 17

​Find the x- and y- intercepts of the graph of the equation   ? ​

Accepted Answer

A)  ​x- intercepts:   ,   ; ​y- intercepts:   
B)  ​​x- intercepts:   ,   ; ​y- intercepts:   
C)  ​​x- intercepts:   ,   ; ​y- intercepts:   ,   
D)  ​​​x- intercepts:   ,   ; ​y- intercepts:   ,   
E)  ​​​x- intercepts:   ; ​y- intercepts:   
A)  ​x- intercepts:   ,   ; ​y- intercepts:   
B)  ​​x- intercepts:   ,   ; ​y- intercepts:   
C)  ​​x- intercepts:   ,   ; ​y- intercepts:   ,   
D)  ​​​x- intercepts:   ,   ; ​y- intercepts:   ,   
E)  ​​​x- intercepts:   ; ​y- intercepts:

Question 18

​Find an equation of the line that passes through the points   and   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 19

​Find the limit: ​
​   ​

Accepted Answer

A)  ​∞ 
B)  ​-∞ 
C)  ​0 
D)  ​-1 
E)  ​1 
A)  ​∞ 
B)  ​-∞ 
C)  ​0 
D)  ​-1 
E)  ​1

Question 20

Describe the interval(s)on which the function   is continuous. ​

Accepted Answer

A)    and   
B)    and   
C)    and   
D)    
E)  none of these choices 
A)    and   
B)    and   
C)    and   
D)    
E)  none of these choices

Write the general form of the equation of the circle with center and solution point

State the signs of and on the interval (0,2).

Use the given information to find of the function , , and

The profit (in dollars)from selling x units of calculus textbooks is given by Find the marginal profit when Round your answer to two decimal places.

For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity.

Use the properties of exponents to simplify the expression

Find the point on the graph of that is closest to the point (8,0.5).Round your answer to two decimal places.

Find all relative maxima of the given function.

Sketch the graph of the function

Find the relative minima,and use a graphing utility to check your results.

Solve the exponential equation.Give the answer correct to 3 decimal places.

Find the slope m and y-intercept b of the line whose equation is given below.

Solve the following equation for x accurate to three decimal places.

Sketch the graph of the equation given below.Use intercepts,extrema,and asymptotes as sketching aids.

Determine the open intervals on which the graph of is concave downward or concave upward.

Find the x- and y- intercepts of the graph of the equation ?

Find an equation of the line that passes through the points and

Find the limit:

Describe the interval(s)on which the function is continuous.

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 1: Functions, graphs, and Limits

Write the general form of the equation of the circle with center and solution point

​State the signs of and on the interval (0,2). ​ ​ ​

​Use the given information to find of the function ​ , , and ​

​The profit (in dollars)from selling x units of calculus textbooks is given by Find the marginal profit when Round your answer to two decimal places. ​

​For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. ​ ​

Use the properties of exponents to simplify the expression ​

​Find the point on the graph of that is closest to the point (8,0.5).Round your answer to two decimal places. ​

​Find all relative maxima of the given function. ​ ​ ​

Sketch the graph of the function ​

​Find the relative minima,and use a graphing utility to check your results. ​ ​

​Solve the exponential equation.Give the answer correct to 3 decimal places. ​ ​

​Find the slope m and y-intercept b of the line whose equation is given below. ​ ​

​Solve the following equation for x accurate to three decimal places. ​ ​

​Sketch the graph of the equation given below.Use intercepts,extrema,and asymptotes as sketching aids. ​ ​ ​

​Determine the open intervals on which the graph of is concave downward or concave upward.

​Find the x- and y- intercepts of the graph of the equation ? ​

​Find an equation of the line that passes through the points and ​

​Find the limit: ​ ​ ​

Describe the interval(s)on which the function is continuous. ​

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

State the signs of and on the interval (0,2).

Use the given information to find of the function , , and

The profit (in dollars)from selling x units of calculus textbooks is given by Find the marginal profit when Round your answer to two decimal places.

For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity.

Use the properties of exponents to simplify the expression

Find the point on the graph of that is closest to the point (8,0.5).Round your answer to two decimal places.

Find all relative maxima of the given function.

Sketch the graph of the function

Find the relative minima,and use a graphing utility to check your results.

Solve the exponential equation.Give the answer correct to 3 decimal places.

Find the slope m and y-intercept b of the line whose equation is given below.

Solve the following equation for x accurate to three decimal places.

Sketch the graph of the equation given below.Use intercepts,extrema,and asymptotes as sketching aids.

Determine the open intervals on which the graph of is concave downward or concave upward.

Find the x- and y- intercepts of the graph of the equation ?

Find an equation of the line that passes through the points and

Find the limit:

Describe the interval(s)on which the function is continuous.