Question 1

​Find   for the following equation: ​   ​

Accepted Answer

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

Question 2

​The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 inch.Use differentials to estimate the propagated error in computing (a)the volume of the cube and (b)the surface area of the cube.Give your answers to two decimal places. ​

Accepted Answer

A)  ​816.48, 151.20 
B)  ​544.32, 136.08 
C)  ​612.36, 136.08 
D)  ​544.32, 120.96 
E)  ​680.40,151.20 
A)  ​816.48, 151.20 
B)  ​544.32, 136.08 
C)  ​612.36, 136.08 
D)  ​544.32, 120.96 
E)  ​680.40,151.20

Question 3

Sketch the graph of the function   ​

Accepted Answer

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

Question 4

A manufacturer charges $80 per unit for units that cost $30 to produce.To encourage large orders from distributors,the manufacturer will reduce the price by $0.01 per unit for each unit in excess of 100 units.(For example,an order of 101 units would have a price of $79.99 per unit,and an order of 102 units would have a price of $79.98 per unit.)This price reduction is discontinued when the price per unit drops to $61.Express the price per unit as a function of the order size. ​​

Accepted Answer

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

Question 5

​Write the following expression as a logarithm of a single quantity. ​   ​

Accepted Answer

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

Question 6

A power station is on one side of a river that is 0.5 mile wide,and a factory is 6 miles downstream on the other side of the river.It costs $14 per foot to run overland power lines and $20 per foot to run underwater power lines.Estimate the value of x that minimizes the cost.The value of   is the length of the overland piece of power line. ​

Accepted Answer

A)  2.56 
B)  5.51 
C)  3 
D)  5.49 
E)  0.87 
A)  2.56 
B)  5.51 
C)  3 
D)  5.49 
E)  0.87

Question 7

Use the graph of   below to sketch     ​

Accepted Answer

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

Question 8

​Compare dy and Δy for   at ​x​ = -1 with Δ​x​ = dx = 0.01.Give your answers to four decimal places. ​

Accepted Answer

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

Question 9

​Locate any relative extrema and inflection points of the function   ​

Accepted Answer

A)  ​relative minimum at   ; inflection point at   
B)  ​relative minimum at   ; no inflection points 
C)  ​no relative maximum or minimum; inflection point at   
D)  ​no relative extrema or inflection points. 
E)  ​relative maximum at   ; inflection point at   
A)  ​relative minimum at   ; inflection point at   
B)  ​relative minimum at   ; no inflection points 
C)  ​no relative maximum or minimum; inflection point at   
D)  ​no relative extrema or inflection points. 
E)  ​relative maximum at   ; inflection point at

Question 10

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

Accepted Answer

A)  ​0.6 
B)  ​2.5 
C)  ​1.25 
D)  ​3.68 
E)  ​does not exist 
A)  ​0.6 
B)  ​2.5 
C)  ​1.25 
D)  ​3.68 
E)  ​does not exist

Question 11

​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 12

​Find the length and width of a rectangle that has perimeter 56 meters and a maximum area. ​​

Accepted Answer

A)  ​7, 21 
B)  ​1, 27 
C)  ​14, 14 
D)  ​15, 13 
E)  ​18,10 
A)  ​7, 21 
B)  ​1, 27 
C)  ​14, 14 
D)  ​15, 13 
E)  ​18,10

Question 13

Find the derivative of the given function. ​   ​

Accepted Answer

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

Question 14

Analytically determine the location(s)of any vertical asymptote(s). ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   ,   
D)  ​   
E)  ​no vertical asymptotes 
A)  ​   
B)  ​   
C)  ​   ,   
D)  ​   
E)  ​no vertical asymptotes

Question 15

​Find the limit:   ​

Accepted Answer

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

Question 16

​The revenue R for a company selling x units is   Use differentials to approximate the change in revenue if sales increase from   to   units. ​

Accepted Answer

A)  ​48,000 dollars 
B)  ​50,000 dollars 
C)  ​45,000 dollars 
D)  ​53,000 dollars 
E)  ​60000 dollars 
A)  ​48,000 dollars 
B)  ​50,000 dollars 
C)  ​45,000 dollars 
D)  ​53,000 dollars 
E)  ​60000 dollars

Question 17

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​
​   ,   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above 
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​none of the above

Question 18

​Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand:   Supply:

Accepted Answer

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

Question 19

​Sketch the graph of the function   using any extrema,intercepts,symmetry,and asymptotes. ​

Accepted Answer

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

Question 20

Find the derivative of the following function. ​   ​

Accepted Answer

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

Find for the following equation:

The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 inch.Use differentials to estimate the propagated error in computing (a)the volume of the cube and (b)the surface area of the cube.Give your answers to two decimal places.

Sketch the graph of the function

Write the following expression as a logarithm of a single quantity.

Use the graph of below to sketch

Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.

Locate any relative extrema and inflection points of the function

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

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

Find the length and width of a rectangle that has perimeter 56 meters and a maximum area.

Find the derivative of the given function.

Analytically determine the location(s)of any vertical asymptote(s).

Find the limit:

The revenue R for a company selling x units is Use differentials to approximate the change in revenue if sales increase from to units.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes.

Find the derivative of the following function.

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

​Find for the following equation: ​ ​

​The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 inch.Use differentials to estimate the propagated error in computing (a)the volume of the cube and (b)the surface area of the cube.Give your answers to two decimal places. ​

Sketch the graph of the function ​

​Write the following expression as a logarithm of a single quantity. ​ ​

Use the graph of below to sketch ​

​Compare dy and Δy for at ​x​ = -1 with Δ​x​ = dx = 0.01.Give your answers to four decimal places. ​

​Locate any relative extrema and inflection points of the function ​

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

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

​Find the length and width of a rectangle that has perimeter 56 meters and a maximum area. ​​

Find the derivative of the given function. ​ ​

Analytically determine the location(s)of any vertical asymptote(s). ​ ​ ​

​Find the limit: ​

​The revenue R for a company selling x units is Use differentials to approximate the change in revenue if sales increase from to units. ​

​Find an equation of the line that is tangent to the graph of f and parallel to the given line. ​ ​ , ​

​Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

​Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. ​

Find the derivative of the following function. ​ ​

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

Find for the following equation:

The measurement of the edge of a cube is found to be 18 inches,with a possible error of 0.7 inch.Use differentials to estimate the propagated error in computing (a)the volume of the cube and (b)the surface area of the cube.Give your answers to two decimal places.

Sketch the graph of the function

Write the following expression as a logarithm of a single quantity.

Use the graph of below to sketch

Compare dy and Δy for at x = -1 with Δx = dx = 0.01.Give your answers to four decimal places.

Locate any relative extrema and inflection points of the function

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

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

Find the length and width of a rectangle that has perimeter 56 meters and a maximum area.

Find the derivative of the given function.

Analytically determine the location(s)of any vertical asymptote(s).

Find the limit:

The revenue R for a company selling x units is Use differentials to approximate the change in revenue if sales increase from to units.

Find an equation of the line that is tangent to the graph of f and parallel to the given line. ,

Find the market equilibrium point for the following demand and supply functions below,where p is price per unit and q is the number of units produced and sold. Demand: Supply:

Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes.

Find the derivative of the following function.