Question 1

Differentiate the

Accepted Answer

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

Question 2

Find a formula for the inverse of the function.

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

Question 3

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 4

If $5000 is invested at 8% interest,find the value of the investment at the end of 4 years if the interest is compounded monthly.

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E)

Question 5

Use the laws of logarithms to expand the expression. ln

Accepted Answer

A)    ln   
B)    ln (x + 5)-   ln (x - 6) 
C)    ln [(x + 5)(x - 6)] 
D)    ln   
A)    ln   
B)    ln (x + 5)-   ln (x - 6) 
C)    ln [(x + 5)(x - 6)] 
D)    ln

Question 6

Find a formula for the inverse of the function.

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E)    
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E)

Question 7

The graph of f is given.Sketch the graph of   on the same set of axes.

Accepted Answer

The answer of The graph of f is given.Sketch the...

Question 8

Find the exponential function   whose graph is given.

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Question 9

Strontium-90 has a half-life of 28 days.A sample has a mass of 50 mg initially.Find a formula for the mass remaining after   days.

Accepted Answer

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E)    
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E)

Question 10

The half-life of cesium -137 is 30 years.Suppose we have a 150-mg sample.Find the mass that remains after   years.

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E)    
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Question 11

If   ,find   .

Accepted Answer

A)  4 
B)  2 
C)  12 
D)  6 
E)  16 
A)  4 
B)  2 
C)  12 
D)  6 
E)  16

Question 12

Evaluate the integral.

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Question 13

Find the derivative of the function.Simplify where possible

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E)

Question 14

Find an equation of the tangent line to the curve   at (1 , 0)

Accepted Answer

The answer of Find an equation of the tangent line...

Question 15

The area of the region that lies to the right of the y-axis and to the left of the parabola   (the shaded region in the figure)is given by the integral  .Find the area..

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Question 16

A telephone line hangs between two poles at 12 m apart in the shape of the catenary   , where x and y are measured in meters.Find the slope of this curve where it meets the right pole.

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E)

Question 17

Use logarithmic differentiation to find the derivative of the function.

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

Question 18

Find the limit.

Accepted Answer

A)    
B)    
C)  0 
D)    
E)  1 
A)    
B)    
C)  0 
D)    
E)  1

Question 19

Assume that is a one-to-one function.
(a)If   ,what is   ?
(b)If   ,what is   ?

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Question 20

Find the exact value of the expression

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Differentiate the function

Find a formula for the inverse of the function.

Find the limit.

If $5000 is invested at 8% interest,find the value of the investment at the end of 4 years if the interest is compounded monthly.

Use the laws of logarithms to expand the expression. ln

Find a formula for the inverse of the function.

The graph of f is given.Sketch the graph of on the same set of axes.

Find the exponential function whose graph is given.

Strontium-90 has a half-life of 28 days.A sample has a mass of 50 mg initially.Find a formula for the mass remaining after days.

The half-life of cesium -137 is 30 years.Suppose we have a 150-mg sample.Find the mass that remains after years.

If ,find .

Evaluate the integral.

Find the derivative of the function.Simplify where possible

Find an equation of the tangent line to the curve at (1 , 0)

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure)is given by the integral .Find the area..

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters.Find the slope of this curve where it meets the right pole.

Use logarithmic differentiation to find the derivative of the function.

Find the limit.

Assume that is a one-to-one function. (a)If ,what is ? (b)If ,what is ?

Find the exact value of the expression

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 5: Integrals

Differentiate the function

Find a formula for the inverse of the function.

Find the limit.

If $5000 is invested at 8% interest,find the value of the investment at the end of 4 years if the interest is compounded monthly.

Use the laws of logarithms to expand the expression. ln

Find a formula for the inverse of the function.

The graph of f is given.Sketch the graph of on the same set of axes.

Find the exponential function whose graph is given.

Strontium-90 has a half-life of 28 days.A sample has a mass of 50 mg initially.Find a formula for the mass remaining after days.

The half-life of cesium -137 is 30 years.Suppose we have a 150-mg sample.Find the mass that remains after years.

If ,find .

Evaluate the integral.

Find the derivative of the function.Simplify where possible

Find an equation of the tangent line to the curve at (1 , 0)

The area of the region that lies to the right of the y-axis and to the left of the parabola (the shaded region in the figure)is given by the integral .Find the area..

A telephone line hangs between two poles at 12 m apart in the shape of the catenary , where x and y are measured in meters.Find the slope of this curve where it meets the right pole.

Use logarithmic differentiation to find the derivative of the function.

Find the limit.

Assume that is a one-to-one function. (a)If ,what is ? (b)If ,what is ?

Find the exact value of the expression

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters