Question 1

The derivative of   is:

Accepted Answer

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

Question 2

Find the limits using L'Hopital's Rule
A)   
B)

Accepted Answer

The answer of Find the limits using L'Hopital's Rule
A) ...

Question 3

How long will it take for your money to double when it is invested at an annual rate of   and compounded yearly? How long will it take for your money to double at an annual rate of   ?

Accepted Answer

11.9 years

Question 4

A drug leaves a person's bloodstream at a rate proportional to the amount present. Assume that half of the initial amount of the drug is still in the bloodstream 4 hours after the dose was given. When is one-tenth of the initial dose remaining in the bloodstream?

Accepted Answer

The answer of A drug leaves a person's bloodstream at...

Question 5

Evaluate the limits using L'Hopital's Rule
A)   
B)

Accepted Answer

The answer of Evaluate the limits using L'Hopital's Rule
A) ...

Question 6

Calculate the definite integrals:
A)   
B)

Accepted Answer

The answer of Calculate the definite integrals:
A)   
B)...

Question 7

At 6:45 a.m., a glass of cold water with initial temperature   C is placed in a room held at   C. If the temperature of the water is   C at 8:15 a.m., when will the water temperature reach   C?

Accepted Answer

The answer of At 6:45 a.m., a glass of cold...

Question 8

A cold chicken with an initial temperature of   C is placed in an oven held at   C. If the temperature of the chicken is   C after 10 min, how much longer after that must the chicken remain in the oven before it reaches   C?

Accepted Answer

29.35 min

Question 9

Evaluate the integral

Accepted Answer

The answer of Evaluate the integral  ...

Question 10

A 1-kg object is dropped from a height of 80 m. After 2 s, the velocity of the object is   m/s. How long after the ball was dropped did the object have a velocity of   m/s?

Accepted Answer

The answer of A 1-kg object is dropped from a...

Question 11

Find   and   such that the line   is tangent to   at   .

Accepted Answer

The answer of Find   and   such...

Question 12

Let   be the inverse of   .
Use the geometric relation between the graphs of inverse functions to compute the integral   .

Accepted Answer

The answer of Let   be the inverse of...

Question 13

Compute the integral   .

Accepted Answer

The answer of Compute the integral   ....

Question 14

Solve:

Accepted Answer

The answer of Solve:  ...

Question 15

Find the derivative of the function at the given point:
A)   
B)   
C)

Accepted Answer

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

Question 16

Solve:

Accepted Answer

The answer of Solve:  ...

Question 17

The function   satisfies the following initial value problem:

Accepted Answer

A)    
B)    
C)    
D)    
E)  none of the above 
A)    
B)    
C)    
D)    
E)  none of the above

Question 18

The integral   is equal to the following algebraic function of   :

Accepted Answer

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

Question 19

Compute the derivatives of the following functions:
A)   
B)   
C)

Accepted Answer

The answer of Compute the derivatives of the following functions:
A)...

Question 20

Let   and suppose the domain of   is restricted to   . Calculate   and   where   is the inverse of   :

Accepted Answer

The answer of Let   and suppose the domain...

The derivative of is:

Find the limits using L'Hopital's Rule A) B)

How long will it take for your money to double when it is invested at an annual rate of and compounded yearly? How long will it take for your money to double at an annual rate of ?

A drug leaves a person's bloodstream at a rate proportional to the amount present. Assume that half of the initial amount of the drug is still in the bloodstream 4 hours after the dose was given. When is one-tenth of the initial dose remaining in the bloodstream?

Evaluate the limits using L'Hopital's Rule A) B)

Calculate the definite integrals: A) B)

At 6:45 a.m., a glass of cold water with initial temperature C is placed in a room held at C. If the temperature of the water is C at 8:15 a.m., when will the water temperature reach C?

A cold chicken with an initial temperature of C is placed in an oven held at C. If the temperature of the chicken is C after 10 min, how much longer after that must the chicken remain in the oven before it reaches C?

Evaluate the integral

A 1-kg object is dropped from a height of 80 m. After 2 s, the velocity of the object is m/s. How long after the ball was dropped did the object have a velocity of m/s?

Find and such that the line is tangent to at .

Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .

Compute the integral .

Solve:

Find the derivative of the function at the given point: A) B) C)

Solve:

The function satisfies the following initial value problem:

The integral is equal to the following algebraic function of :

Compute the derivatives of the following functions: A) B) C)

Let and suppose the domain of is restricted to . Calculate and where is the inverse of :

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

Exam 7: Exponential Functions

The derivative of is:

Find the limits using L'Hopital's Rule A) B)

How long will it take for your money to double when it is invested at an annual rate of and compounded yearly? How long will it take for your money to double at an annual rate of ?

A drug leaves a person's bloodstream at a rate proportional to the amount present. Assume that half of the initial amount of the drug is still in the bloodstream 4 hours after the dose was given. When is one-tenth of the initial dose remaining in the bloodstream?

Evaluate the limits using L'Hopital's Rule A) B)

Calculate the definite integrals: A) B)

At 6:45 a.m., a glass of cold water with initial temperature C is placed in a room held at C. If the temperature of the water is C at 8:15 a.m., when will the water temperature reach C?

A cold chicken with an initial temperature of C is placed in an oven held at C. If the temperature of the chicken is C after 10 min, how much longer after that must the chicken remain in the oven before it reaches C?

Evaluate the integral

A 1-kg object is dropped from a height of 80 m. After 2 s, the velocity of the object is m/s. How long after the ball was dropped did the object have a velocity of m/s?

Find and such that the line is tangent to at .

Let be the inverse of . Use the geometric relation between the graphs of inverse functions to compute the integral .

Compute the integral .

Solve:

Find the derivative of the function at the given point: A) B) C)

Solve:

The function satisfies the following initial value problem:

The integral is equal to the following algebraic function of :

Compute the derivatives of the following functions: A) B) C)

Let and suppose the domain of is restricted to . Calculate and where is the inverse of :

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters