Question 1

The half-life of cesium-  is  years. Suppose we have a  -mg sample. How much of the sample remains after  years?

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 2

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Find the limit.

Accepted Answer

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

Question 4

Evaluate the limit using l'Hôpital's Rule.

Accepted Answer

A) 75 
B) 25 
C) 15 
D)

Question 5

Solve each equation for x.(a)  (b)

Accepted Answer

The answer of Solve each equation for x.(a)  (b)...

Question 6

The graph of f is given. Sketch the graph of  on the same set of axes.  3

Accepted Answer

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

Question 7

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

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

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

Question 9

Find the numerical value of the expression.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

Find the exact value of the expression.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 11

Find the derivative of the function. Simplify where possible.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Use the laws of logarithms to write the expression as the logarithm of a single quantity.4 ln 5 -  ln (x + 6)

Accepted Answer

A)   
B)   
C)   
D)

Question 13

Find the value of the expression accurate to four decimal places.sinh 4

Accepted Answer

A) 29.3082 
B) 55.5798 
C) 15.145 
D) 27.2899

Question 14

Starting with the graph of  , find the equation of the graph that results from reflecting about the line  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 15

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 3 ft? Rounded to the nearest mile.

Accepted Answer

A) 13,014,952 mi 
B) 13015052.4 mi 
C) 5.2 mi 
D) 13,015,152 mi 
E) 1084587.7 mi

Question 16

Find the exponential function  whose graph is given.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 17

Find the domain, range, and x-intercept(s) of the function.

Accepted Answer

The answer of Find the domain, range, and x-intercept(s) of...

Question 18

If  is invested at  interest, find the value of the investment at the end of  years if the interest is compounded  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 19

Find an equation of the tangent line to the curve  at  .

Accepted Answer

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

Question 20

Determine whether f is one-to-one.

Accepted Answer

The answer of Determine whether f is one-to-one. ...

Exam 3: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

The half-life of cesium- is years. Suppose we have a -mg sample. How much of the sample remains after years?

Use logarithmic differentiation to find the derivative of the function.

Find the limit.

Evaluate the limit using l'Hôpital's Rule.

Solve each equation for x.(a) (b)

The graph of f is given. Sketch the graph of on the same set of axes. 3

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

Use the laws of logarithms to expand the expression.ln

Find the numerical value of the expression.

Find the exact value of the expression.

Find the derivative of the function. Simplify where possible.

Use the laws of logarithms to write the expression as the logarithm of a single quantity.4 ln 5 - ln (x + 6)

Find the value of the expression accurate to four decimal places.sinh 4

Starting with the graph of , find the equation of the graph that results from reflecting about the line .

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 3 ft? Rounded to the nearest mile.

Find the exponential function whose graph is given.

Find the domain, range, and x-intercept(s) of the function.

If is invested at interest, find the value of the investment at the end of years if the interest is compounded .

Find an equation of the tangent line to the curve at .

Determine whether f is one-to-one.