Question 1

Use transformations to sketch the graph of the function.

Accepted Answer

The answer of Use transformations to sketch the graph of...

Question 2

Find the limit.

Accepted Answer

The answer of Find the limit. ...

Question 3

Use logarithmic differentiation to find the derivative of the function. y = (x + 7)^5/^x

Accepted Answer

The answer of Use logarithmic differentiation to find the derivative...

Question 4

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places.
f (x) = 0.2x  - 1.8x - 3.8; g(x) = -0.1x  + 0.8x + 6.7

Accepted Answer

The answer of Find the points of intersection of the...

Question 5

Differentiate the function.

Accepted Answer

The answer of Differentiate the function. ...

Question 6

Evaluate the given integral.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Suppose g is the inverse function of a differentiable function f and  .
If

Accepted Answer

The answer of Suppose g is the inverse function of...

Question 8

Find the derivative of y.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 9

Find, correct to three decimal places the area of the region above the hyperbola  , below the x axis, and between the lines x = - 4 and x = - 3.

Accepted Answer

The answer of Find, correct to three decimal places the...

Question 10

Differentiate the function. g(x) =

Accepted Answer

A)   
B)   
C)   
D)

Question 11

A painting in an art gallery has height h and is hung so that lower edge is a distance d above the eye of an observer (as in the figure). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so as to maximize the angle  subtended at his eye by the painting?)

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Find the derivative of the function. f (x) = 6 tan^-¹x²

Accepted Answer

The answer of Find the derivative of the function.
f (x)...

Question 13

Suppose that the graph of  is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches  ft.

Accepted Answer

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

Question 14

Find

Accepted Answer

A)   
B)   
C)   
D)   
E) none of these

Question 15

Find

Accepted Answer

The answer of Find  ...

Question 16

Find

Accepted Answer

The answer of Find  ...

Question 17

Evaluate the limit using l'Hôpital's Rule.

Accepted Answer

A) 6 
B) 12 
C)   
D) 4

Question 18

Strontium-  has a half-life of  days. A sample has a mass of  mg initially. Find the mass remaining after 38 days.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find the values of  for which  satisfies the equation

Accepted Answer

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

Question 20

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.

Accepted Answer

A)   
B)   
C)   
D)  sinh 6 
E)

Exam 6: Inverse Functions

Use transformations to sketch the graph of the function.

Find the limit.

Use logarithmic differentiation to find the derivative of the function. y = (x + 7)5/x

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.2x - 1.8x - 3.8; g(x) = -0.1x + 0.8x + 6.7

Differentiate the function.

Evaluate the given integral.

Suppose g is the inverse function of a differentiable function f and . If

Find the derivative of y.

Find, correct to three decimal places the area of the region above the hyperbola , below the x axis, and between the lines x = - 4 and x = - 3.

Differentiate the function. g(x) =

Find the derivative of the function. f (x) = 6 tan-1 x2

Suppose that the graph of is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches ft.

Find

Find

Find

Evaluate the limit using l'Hôpital's Rule.

Strontium- has a half-life of days. A sample has a mass of mg initially. Find the mass remaining after 38 days.

Find the values of for which satisfies the equation

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. y = (x + 7)^5/^x

Find the derivative of the function. f (x) = 6 tan^-¹x²