Question 1

Find the limit   , if it exists.

Accepted Answer

The answer of Find the limit   , if...

Question 2

The geologist C. F. Richter defined the magnitude of an earthquake to be   where I is the intensity of the quake (measured by the amplitude of a seismograph 100 km from the epicenter) and S is the intensity of a "standard" earthquake (where the amplitude is only   cm). The 1989 Loma Prieta earthquake that shook San Francisco had a magnitude of   on the Richter scale. The 1906 San Francisco earthquake was   times as intense. What was its magnitude on the Richter scale?

Accepted Answer

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

Question 3

If a bacteria population starts with 50 bacteria and doubles every three hours, then the number of bacteria after t hours is   . When will the population reach   ?

Accepted Answer

The answer of If a bacteria population starts with 50...

Question 4

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

Accepted Answer

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

Question 5

Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 3 -   ln (x + 3)

Accepted Answer

A) ln   
B)    
C) ln 34 - ln (x + 3)3/4 
D)    
A) ln   
B)    
C) ln 34 - ln (x + 3)3/4 
D)

Question 6

Use logarithmic differentiation to find the derivative of the function.

Accepted Answer

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

Question 7

Find f -1 (a) for the function f and the real number a. f (x) = x3 + x - 7; a = -5

Accepted Answer

A) 0 
B) 3 
C) 2 
D) 1 
A) 0 
B) 3 
C) 2 
D) 1

Question 8

Find the inverse of F. Then sketch the graphs of f and f -1 on the same set of axes.f (x) =   , x $\ge$ 0

Accepted Answer

A) f -1(x) = -   , x $\ge$ 0   
B) f -1(x) =   , x $\ge$ 0   
C) f -1(x) =   , x $\ge$ 0   
D) f -1(x) = -   , x $\ge$ 0   
A) f -1(x) = -   , x $\ge$ 0   
B) f -1(x) =   , x $\ge$ 0   
C) f -1(x) =   , x $\ge$ 0   
D) f -1(x) = -   , x $\ge$ 0

Question 9

Use Newton's method to find the roots of the equation correct to five decimal places. x ln x - 1 = 0

Accepted Answer

A) 0.88161 
B) 1.76322 
C) 2.26322 
D) 1.26322 
A) 0.88161 
B) 1.76322 
C) 2.26322 
D) 1.26322

Question 10

Find the limit.

Accepted Answer

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

Question 11

Write the expression as an exponent with base

Accepted Answer

A) e (tan 6x) 
B) e (tan x) (ln 6) 
C) e (6 tan x)  
D) 6e (tan x)  
E) 6 tan x 
A) e (tan 6x) 
B) e (tan x) (ln 6) 
C) e (6 tan x)  
D) 6e (tan x)  
E) 6 tan x

Question 12

Find the derivative of

Accepted Answer

The answer of Find the derivative of   ...

Question 13

Find the inverse of the function.

Accepted Answer

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

Question 14

Express the quantity as a single logarithm.

Accepted Answer

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

Question 15

Sketch a graph of the function.
f (x) =

Accepted Answer

The answer of Sketch a graph of the function.
f (x)...

Question 16

Find the exact value of the given expression. sin-1

Accepted Answer

A)    
B) $\pi$ 
C)    
D) 2$\pi$ 
A)    
B) $\pi$ 
C)    
D) 2$\pi$

Question 17

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

Accepted Answer

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

Question 18

Determine whether f is one-to-one.

Accepted Answer

A) True 
 B)False

Question 19

Find the exponential function   whose graph is given.

Accepted Answer

The answer of Find the exponential function   whose...

Question 20

Solve the equation for x.

Accepted Answer

The answer of Solve the equation for x.  ...

Find the limit , if it exists.

If a bacteria population starts with 50 bacteria and doubles every three hours, then the number of bacteria after t hours is . When will the population reach ?

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

Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 3 - ln (x + 3)

Use logarithmic differentiation to find the derivative of the function.

Find f ^-¹(a) for the function f and the real number a. f (x) = x³ + x - 7; a = -5

Find the inverse of F. Then sketch the graphs of f and f ^-¹ on the same set of axes.f (x) = $Find the inverse of F. Then sketch the graphs of f and f <sup>-</sup><sup>1</sup> on the same set of axes.f (x) = , x \ge 0$ , x $\ge$ 0

Use Newton's method to find the roots of the equation correct to five decimal places. x ln x - 1 = 0

Find the limit.

Write the expression as an exponent with base

Find the derivative of

Find the inverse of the function.

Express the quantity as a single logarithm.

Sketch a graph of the function. f (x) =

Find the exact value of the given expression. sin^-¹

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

Determine whether f is one-to-one.

Find the exponential function whose graph is given.

Solve the equation for x.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 6: Inverse Functions

Find the limit , if it exists.

If a bacteria population starts with 50 bacteria and doubles every three hours, then the number of bacteria after t hours is . When will the population reach ?

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

Use the laws of logarithms to write the expression as the logarithm of a single quantity. 4 ln 3 - ln (x + 3)

Use logarithmic differentiation to find the derivative of the function.

Find f -1 (a) for the function f and the real number a. f (x) = x3 + x - 7; a = -5

Find the inverse of F. Then sketch the graphs of f and f -1 on the same set of axes.f (x) = , x ≥\ge≥ 0

Use Newton's method to find the roots of the equation correct to five decimal places. x ln x - 1 = 0

Find the limit.

Write the expression as an exponent with base

Find the derivative of

Find the inverse of the function.

Express the quantity as a single logarithm.

Sketch a graph of the function. f (x) =

Find the exact value of the given expression. sin-1

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

Determine whether f is one-to-one.

Find the exponential function whose graph is given.

Solve the equation for x.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Find f ^-¹(a) for the function f and the real number a. f (x) = x³ + x - 7; a = -5

Find the inverse of F. Then sketch the graphs of f and f ^-¹ on the same set of axes.f (x) = $Find the inverse of F. Then sketch the graphs of f and f <sup>-</sup><sup>1</sup> on the same set of axes.f (x) = , x \ge 0$ , x $\ge$ 0

Find the exact value of the given expression. sin^-¹