Question 1

In the following figure,  gives the population  of a certain bacteria culture at time t after a portion of bactericide A was introduced into the population at  . The graph of g gives the population  of a similar bacteria culture at time t after a portion of bactericide B was introduced into the population at  .  Which population is decreasing faster at  ?
Population __________
Which population is decreasing faster at  ?
Population __________
Which bactericide is more effective in reducing the population of bacteria in the short run?
Bactericide __________
Which bactericide is more effective in reducing the population of bacteria in the long run?
Bactericide __________

Accepted Answer

The answer of In the following figure,  gives the...

Question 2

Find  for the function. Simplify your answer.

Accepted Answer

The answer of Find  for the function. Simplify your...

Question 3

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 population growth at  min.

Accepted Answer

A)  148 bacteria per minute 
B)  113 bacteria per minute 
C)  125 bacteria per minute 
D)  120 bacteria per minute

Question 4

Use the graph of the function f to find  and  if the limit exists. If it does not, answer none.   __________  __________  __________

Accepted Answer

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

Question 5

Let  ,  . Find the rule for the function

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

Determine whether the equation defines y as a linear function of x.

Accepted Answer

A)  No, the equation does not define y as a linear function of x 
B)  Yes, the equation defines y as a linear function of x

Question 7

Let f be the function defined by f (x) = 8x + 9. Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Accepted Answer

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

Question 8

Find the one-sided limit.

Accepted Answer

The answer of Find the one-sided limit. ...

Question 9

Find functions f and g such that  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Evaluate h (3), where    Round the answer to two decimal places, if necessary
h (3) = __________

Accepted Answer

The answer of Evaluate h (3), where   ...

Question 11

Let f be the function defined by  Find    and

Accepted Answer

A)

B)

C)

D)

E)

Question 12

A function f is continuous at the point  if the following conditions are satisfied. 1.  is defined.
2)  exists.
3)  .
Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Accepted Answer

A)   
B)   
C)   
D)   
E)  Continuous everywhere

Question 13

Find  given that  and  .

Accepted Answer

The answer of Find  given that  and ...

Question 14

Ace Truck leases its 10-ft box truck at $35/day and $0.45/mi, whereas Acme Truck leases a similar truck at $30/day and $0.50/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

Accepted Answer

The answer of Ace Truck leases its 10-ft box truck...

Question 15

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

Accepted Answer

A)   
B)   
C)   
D)

Question 16

The number of homes with digital TVs is expected to grow according to the function  where t is measured in years, with t = 0 corresponding to the beginning of 2000, and f(t) is measured in millions of homes.
Round your answers to the nearest whole number.
How many homes had digital TVs at the beginning of 2000?
__________
How many homes will have digital TVs at the beginning of 2005?
__________

Accepted Answer

The answer of The number of homes with digital TVs...

Question 17

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

Question 18

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

Accepted Answer

The answer of Find the values of x for which...

Question 19

Let  . Find the zeros of f in  by solving the equation  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 20

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.
__________

Accepted Answer

The answer of Let  .
Find the derivative  of...

Exam 2: Functions, Limits and the Derivative

Find for the function. Simplify your answer.

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 population growth at min.

Use the graph of the function f to find and if the limit exists. If it does not, answer none. __

Let , . Find the rule for the function

Determine whether the equation defines y as a linear function of x.

Let f be the function defined by f (x) = 8x + 9. Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Find the one-sided limit.

Find functions f and g such that .

Evaluate h (3), where Round the answer to two decimal places, if necessary h (3) = __________

Let f be the function defined by Find and

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2) exists. 3) . Determine the values of x, if any, at which the function is discontinuous. At each point of discontinuity, state the condition(s) for continuity that are violated.

Find given that and .

Ace Truck leases its 10-ft box truck at $35/day and $0.45/mi, whereas Acme Truck leases a similar truck at $30/day and $0.50/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

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

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?

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

Let . Find the zeros of f in by solving the equation .

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. __