Question 1

Find   by implicit differentiation.

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Question 2

Find the differential of the function.

Accepted Answer

The answer of Find the differential of the function. ...

Question 3

Suppose   . Find   given that   ,   ,   ,   .

Accepted Answer

The answer of Suppose   . Find  ...

Question 4

Find the derivative of the function by using the rules of differentiation.

Accepted Answer

The answer of Find the derivative of the function by...

Question 5

Find   by implicit differentiation.

Accepted Answer

The answer of Find   by implicit differentiation. ...

Question 6

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation   . The weekly total cost incurred by Pulsar for producing x sets is   dollars. Compute   ,   ,   .

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Question 7

Let   . Find   .

Accepted Answer

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Question 8

The demand function for a certain make of exercise bicycle sold exclusively through cable television is   , where p is the unit price in hundreds of dollars and x is the quantity demanded/week. Compute the elasticity of demand and determine the range of prices corresponding to inelastic, unitary, and elastic demand.

Accepted Answer

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Question 9

Find the derivative of the function.

Accepted Answer

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Question 10

Find the derivative of the function.

Accepted Answer

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Question 11

The demand function for a certain brand of compact disc is   , where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand.
Compute the elasticity of demand (to the nearest hundredth) when x = 10.
__________
Determine whether the demand is inelastic, unitary, or elastic when x = 10.
__________

Accepted Answer

The answer of The demand function for a certain brand...

Question 12

Find the derivative of the function by using the rules of differentiation.

Accepted Answer

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Question 13

The supply function for a certain make of transistor radio is given by   , where x is the quantity supplied and p is the unit price in dollars. What is the rate of change of the unit price if the quantity supplied is 100,000 transistor radios?

Accepted Answer

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Question 14

Determine whether the statement is true or false.
If f is differentiable, then   .

Accepted Answer

The answer of Determine whether the statement is true or...

Question 15

Find the first and second derivatives of the function.

Accepted Answer

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Question 16

Find   .

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Question 17

In calm waters oil spilling from the ruptured hull of a grounded tanker spreads in all directions. If the area polluted is a circle and its radius is increasing at a rate of 3 ft/sec, determine how fast the area is increasing when the radius of the circle is 70 ft.

Accepted Answer

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Question 18

The total worldwide box-office receipts for a long-running movie are approximated by the function   , where   is measured in millions of dollars and x is the number of years since the movie's release. How fast are the total receipts changing 1 yr, 3 yr, and 5 yr after its release?

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Question 19

A study prepared for the National Association of Realtors estimates that the number of housing starts per year over the next 5 yr will be   million units, where r (percent) is the mortgage rate. Use differentials to estimate the decrease in the number of housing starts when the mortgage rate is increased from 10% to 10.6%. Round to the nearest unit.
Give your answer as a number without the units.

Accepted Answer

The answer of A study prepared for the National Association...

Question 20

Find the first and second derivatives of the function.

Accepted Answer

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Find by implicit differentiation.

Find the differential of the function.

Suppose . Find given that , , , .

Find the derivative of the function by using the rules of differentiation.

Find by implicit differentiation.

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , .

Let . Find .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

The supply function for a certain make of transistor radio is given by , where x is the quantity supplied and p is the unit price in dollars. What is the rate of change of the unit price if the quantity supplied is 100,000 transistor radios?

Determine whether the statement is true or false. If f is differentiable, then .

Find the first and second derivatives of the function.

Find .

In calm waters oil spilling from the ruptured hull of a grounded tanker spreads in all directions. If the area polluted is a circle and its radius is increasing at a rate of 3 ft/sec, determine how fast the area is increasing when the radius of the circle is 70 ft.

The total worldwide box-office receipts for a long-running movie are approximated by the function , where is measured in millions of dollars and x is the number of years since the movie's release. How fast are the total receipts changing 1 yr, 3 yr, and 5 yr after its release?

Find the first and second derivatives of the function.

Preliminaries

Functions, Limits and the Derivative

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 3: Differentiation

Find by implicit differentiation.

Find the differential of the function.

Suppose . Find given that , , , .

Find the derivative of the function by using the rules of differentiation.

Find by implicit differentiation.

Pulsar manufactures a series of 19-in. color television sets. The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation . The weekly total cost incurred by Pulsar for producing x sets is dollars. Compute , , .

Let . Find .

Find the derivative of the function.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

The supply function for a certain make of transistor radio is given by , where x is the quantity supplied and p is the unit price in dollars. What is the rate of change of the unit price if the quantity supplied is 100,000 transistor radios?

Determine whether the statement is true or false. If f is differentiable, then .

Find the first and second derivatives of the function.

Find .

In calm waters oil spilling from the ruptured hull of a grounded tanker spreads in all directions. If the area polluted is a circle and its radius is increasing at a rate of 3 ft/sec, determine how fast the area is increasing when the radius of the circle is 70 ft.

The total worldwide box-office receipts for a long-running movie are approximated by the function , where is measured in millions of dollars and x is the number of years since the movie's release. How fast are the total receipts changing 1 yr, 3 yr, and 5 yr after its release?

Find the first and second derivatives of the function.

Preliminaries

Functions, Limits and the Derivative

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters