Question 1

Find the indicated one-sided limit.

Accepted Answer

A) 81 
B) 0 
C) -18 
D)    
E)    
A) 81 
B) 0 
C) -18 
D)    
E)

Question 2

The volume of a spherical cancerous tumor is given by the function   where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is decuple?

Accepted Answer

The answer of The volume of a spherical cancerous tumor...

Question 3

Let   . Find the derivative   of   and the point on the graph of   where the tangent line to the curve is horizontal.

Accepted Answer

A)    ; (   ) 
B)    ; (   ) 
C)    ; (   ) 
D)    ; (   ) 
E)    ; (   ) 
A)    ; (   ) 
B)    ; (   ) 
C)    ; (   ) 
D)    ; (   ) 
E)    ; (   )

Question 4

The circumference of a circle is given by   where r is the radius of the circle.What is the circumference of a circle with a 6-in.radius?

Accepted Answer

The answer of The circumference of a circle is given...

Question 5

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function   Find the rate of the population growth at t = 30 min.

Accepted Answer

A) 3 bacteria per minute 
B) 30 bacteria per minute 
C) 180 bacteria per minute 
D) 2 bacteria per minute 
E) 123 bacteria per minute 
A) 3 bacteria per minute 
B) 30 bacteria per minute 
C) 180 bacteria per minute 
D) 2 bacteria per minute 
E) 123 bacteria per minute

Question 6

Find the values of x for which the function is continuous.

Accepted Answer

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

Question 7

Let   .Find the rule for the function   .

Accepted Answer

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

Question 8

Find the limit.

Accepted Answer

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

Question 9

Let   and   .Find the rule for the function   .

Accepted Answer

The answer of Let   and   .Find...

Question 10

Let f be the function defined by f (x) = 7x + 8.Find         and

Accepted Answer

The answer of Let f be the function defined by...

Question 11

Let   .
Find the derivative   of   .   __________
Find the point on the graph of f where the tangent line to the curve is horizontal.
__________
Sketch the graph of f and the tangent line to the curve at the point where the tangent line to the curve is horizontal.
Select the correct graph by entering A, B, or 
C.__________

Let
   represent the point on the graph of f where the tangent line to the curve is horizontal.What is the rate of change of f at this point?
   __________

Accepted Answer

The answer of Let   .
Find the derivative ...

Question 12

The volume of a spherical cancerous tumor is given by the function   where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is quintuple?

Accepted Answer

A) 78,125 
B) 625 
C) 125 
D) 5 
E) 25 
A) 78,125 
B) 625 
C) 125 
D) 5 
E) 25

Question 13

Let   ,   , and   Find the rule for the function fgh.

Accepted Answer

The answer of Let   ,   ,...

Question 14

For the demand equation   where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Accepted Answer

A) x = 9,000 units 
B) x = 4,500 units 
C) x = 90 units 
D) x = 3,000 units 
E) x = 900 units 
A) x = 9,000 units 
B) x = 4,500 units 
C) x = 90 units 
D) x = 3,000 units 
E) x = 900 units

Question 15

Find   given that   and   .

Accepted Answer

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

Question 16

Use the graph of the function f to determine   and

Accepted Answer

The answer of Use the graph of the function f...

Question 17

The following graph shows the volume of wood produced in a single-species forest.Here   is measured in cubic meters/hectare and t is measured in years.By computing the slopes of the respective tangent lines, estimate the rate at which the wood grown is changing at the beginning of year 10 and at the beginning of year 35.

Accepted Answer

A)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
B)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
C)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
D)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
A)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
B)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
C)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35 
D)    cubic meters/hectare per year in the year 10,

cubic meters/hectare per year in the year 35

Question 18

Find the limit, if it exists.

Accepted Answer

A)    
B)    
C)    
D) The limit does not exist 
A)    
B)    
C)    
D) The limit does not exist

Question 19

A study of driving costs of 1992 model subcompact (four-cylinder) cars found that the average cost (car payments, gas, insurance, upkeep, and depreciation), measured in cents/mile, is approximated by the function   where x denotes the number of miles (in thousands) the car is driven in a year.What happens to the average cost as the number of miles driven increases without bound?

Accepted Answer

A) It approaches 15.39   . 
B) It approaches 2,290   . 
C) It increases without bound. 
D) It becomes infinitely small. 
A) It approaches 15.39   . 
B) It approaches 2,290   . 
C) It increases without bound. 
D) It becomes infinitely small.

Question 20

Find the domain of the function

Accepted Answer

The answer of Find the domain of the function ...

Find the indicated one-sided limit.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is decuple?

Let . Find the derivative of and the point on the graph of where the tangent line to the curve is horizontal.

The circumference of a circle is given by where r is the radius of the circle.What is the circumference of a circle with a 6-in.radius?

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function Find the rate of the population growth at t = 30 min.

Find the values of x for which the function is continuous.

Let .Find the rule for the function .

Find the limit.

Let and .Find the rule for the function .

Let f be the function defined by f (x) = 7x + 8.Find and

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is quintuple?

Let , , and Find the rule for the function fgh.

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Find given that and .

Use the graph of the function f to determine and

Find the limit, if it exists.

Find the domain of the function

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 2: Functions, Limits and the Derivative

Find the indicated one-sided limit.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is decuple?

Let . Find the derivative of and the point on the graph of where the tangent line to the curve is horizontal.

The circumference of a circle is given by where r is the radius of the circle.What is the circumference of a circle with a 6-in.radius?

Under a set of controlled laboratory conditions, the size of the population of a certain bacteria culture at time t (in minutes) is described by the function Find the rate of the population growth at t = 30 min.

Find the values of x for which the function is continuous.

Let .Find the rule for the function .

Find the limit.

Let and .Find the rule for the function .

Let f be the function defined by f (x) = 7x + 8.Find and

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters.By what factor is the volume of the tumor increased if its radius is quintuple?

Let , , and Find the rule for the function fgh.

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Find given that and .

Use the graph of the function f to determine and

Find the limit, if it exists.

Find the domain of the function

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters