Question 1

Find function f such that   and

Accepted Answer

The answer of Find function f such that  ...

Question 2

Use the graph of the given function f to determine  at the indicated value of a, if it exists.

Accepted Answer

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

Question 3

The number of IBM shares that Nancy owns is given by f (t). The price per share of the stock of IBM at time t is g(t) dollars. What does the function f (t)g(t) represent?

Accepted Answer

A)  The value in dollars of Nancy's shares of IBM at time t 
B)  The total number of IBM shares at time t 
C)  The number of IBM shares that Nancy owns at time t 
D)  The price per share of the stock of IBM at time t

Question 4

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,900 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Accepted Answer

A)  C(x) = 0.5x 
B)  C(x) = 0.5x + 10,900 
C)  C(x) = 10,900x + 0.5 
D)  C(x) = (0.5 + 10,900)x 
E)  C(x) = 10,900x

Question 5

Find the rules for the composite functions  and

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 6

The gross domestic product (GDP) of a certain country is projected to be  billion dollars t yr from now.
What will be the rate of change of the country's GDP 3 yr from now?
$ __________ billion/yr
What will be the rate of change of the country's GDP 5 yr from now?
$ __________ billion/yr

Accepted Answer

The answer of The gross domestic product (GDP) of a...

Question 7

For the pair of supply and demand equations  where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Accepted Answer

A)  x = 11.5, p = $96.50 
B)  x = 18.5, p = $233.50 
C)  x = 15, p = $135.00 
D)  x = 3.5, p = $68.50 
E)  x = 18.5, p = $173.50

Question 8

Find the indicated limit, if it exists. Otherwise, answer no solution.

Accepted Answer

The answer of Find the indicated limit, if it exists....

Question 9

Refer to the graph of the function f in the following figure.  Find the value of x for which f (x) = 2 and f (x) = 0.

Accepted Answer

The answer of Refer to the graph of the function...

Question 10

The 1980s saw a trend toward old-fashioned punitive deterrence as opposed to the more liberal penal policies and community-based corrections popular in the 1960s and early 1970s. As a result, prisons became more crowded, and the gap between the number of people in prison and the prison capacity widened. The number of prisoners (in thousands) in federal and state prisons is approximated by the function  where t is measured in years, with t = 0 corresponding to 1983. The number of inmates for which prisons were designed is given by  where C(t) is measured in thousands and t has the same meaning as before. Find an expression that shows the gap between the number of prisoners and the number of inmates for which the prisons were designed at any time t.

Accepted Answer

The answer of The 1980s saw a trend toward old-fashioned...

Question 11

Use the vertical-line test to determine whether the graph represents y as a function of x.

Accepted Answer

A)  No, the graph does not represent y as a function of x. 
B)  Yes, the graph represents y as a function of x.

Question 12

Find the domain of the function

Accepted Answer

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

Question 13

Let   and  . Find the rule for the function

Accepted Answer

The answer of Let   and  . Find...

Question 14

Productivity and yield of cultivated crops are often reduced by insect pests. The following graph shows the relationship between the yield of a certain crop,  , as a function of the density of aphids x. (Aphids are small insects that suck plant juices.) Here,  is measured in kilograms/ 4,000 square meters, and x is measured in hundreds of aphids/bean stem. By computing the slopes of the respective tangent lines, estimate the rate of change of the crop yield with respect to the density of aphids when that density is 200 aphids/bean stem and when it is 800 aphids/bean stem.

Accepted Answer

The answer of Productivity and yield of cultivated crops are...

Question 15

A function f is continuous at the point  if the following conditions are satisfied.
1.  is defined.
2.  exists.
3.  .
Determine the value of x, if any, at which the function is discontinuous.    __________
State the condition(s) for continuity that are violated.
Conditions: __________

Accepted Answer

The answer of A function f is continuous at the...

Question 16

Let h be the function defined by  . Find h(8), h(0), h(a) and h(  a).

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find f (a + h) - f (a) for the function f (x) = 2x + 4. Simplify your answer.

Accepted Answer

The answer of Find f (a + h) - f...

Question 18

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is  the crickets chirp at the rate of 120 times/minute, and when the temperature is  they chirp at the rate of 160 times/minute. Find an equation giving the relationship between the air temperature T and the number of chirps/minute N of the crickets.

Accepted Answer

The answer of Entomologists have discovered that a linear relationship...

Question 19

Use the method of bisection to find the root of the equation  , accurate to two decimal places if necessary.  __________

Accepted Answer

The answer of Use the method of bisection to find...

Question 20

Joan is looking straight out a window of an apartment building at a height of 30 ft from the ground. A boy throws a tennis ball straight up by the side of the building where the window is located. Suppose the height of the ball (measured in feet) from the ground at time t is  At what time(s) does the ball cross Joan's line of sight?

Accepted Answer

The answer of Joan is looking straight out a window...

Exam 2: Functions, Limits and the Derivative

Find function f such that and

Use the graph of the given function f to determine at the indicated value of a, if it exists.

The number of IBM shares that Nancy owns is given by f (t) . The price per share of the stock of IBM at time t is g(t) dollars. What does the function f (t) g(t) represent?

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,900 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Find the rules for the composite functions and

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ billion/yr

For the pair of supply and demand equations where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Find the indicated limit, if it exists. Otherwise, answer no solution.

Refer to the graph of the function f in the following figure. Find the value of x for which f (x) = 2 and f (x) = 0.

Use the vertical-line test to determine whether the graph represents y as a function of x.

Find the domain of the function

Let and . Find the rule for the function

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions:

Let h be the function defined by . Find h(8) , h(0) , h(a) and h( a) .

Find f (a + h) - f (a) for the function f (x) = 2x + 4. Simplify your answer.

Use the method of bisection to find the root of the equation , accurate to two decimal places if necessary. __________

Exam 2: Functions, Limits and the Derivative

Find function f such that and

Use the graph of the given function f to determine at the indicated value of a, if it exists.

The number of IBM shares that Nancy owns is given by f (t) . The price per share of the stock of IBM at time t is g(t) dollars. What does the function f (t) g(t) represent?

TMI, a manufacturer of blank audiocassette tapes, has a monthly fixed cost of $10,900 and a variable cost of $0.50/tape. Find a function C that gives the total cost incurred by TMI in the manufacture of x tapes/month.

Find the rules for the composite functions and

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ __________ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ __________ billion/yr

For the pair of supply and demand equations where x represents the quantity demanded in units of a thousand and p the unit price in dollars, find the equilibrium quantity and the equilibrium price.

Find the indicated limit, if it exists. Otherwise, answer no solution.

Refer to the graph of the function f in the following figure. Find the value of x for which f (x) = 2 and f (x) = 0.

Use the vertical-line test to determine whether the graph represents y as a function of x.

Find the domain of the function

Let and . Find the rule for the function

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. __________ State the condition(s) for continuity that are violated. Conditions: __________

Let h be the function defined by . Find h(8) , h(0) , h(a) and h( a) .

Find f (a + h) - f (a) for the function f (x) = 2x + 4. Simplify your answer.

Use the method of bisection to find the root of the equation , accurate to two decimal places if necessary. __________

The gross domestic product (GDP) of a certain country is projected to be billion dollars t yr from now. What will be the rate of change of the country's GDP 3 yr from now? $ billion/yr What will be the rate of change of the country's GDP 5 yr from now? $ billion/yr

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions: