Question 1

Evaluate the integral.
-  dx

Accepted Answer

A)    
B)    - 1 
C)    + C 
D)    
A)    
B)    - 1 
C)    + C 
D)

Question 2

Evaluate the definite integral.
-

Accepted Answer

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

Question 3

Determine the indefinite integral.
-  , x < ln 4

Accepted Answer

A)        + C 
B)  -       + C 
C)  -       + C 
D)      + C 
A)        + C 
B)  -       + C 
C)  -       + C 
D)      + C

Question 4

Solve the problem.
-When an object falling from rest encounters air resistance proportional to the square of its velocity, the distance it falls (in meters) after t seconds is given by   where m is the mass of the object in kilograms, g = 9.8 m/sS1U1P12S1S1P0  is the acceleration due to gravity, and k is a physical constant. A BASE jumper (m = 76kg)  leaps from a tall cliff and performs a ten-second delay (she free falls for 10 s and then opens her chute). How far does she fall in 10 s? Assume   k = 0.2 Round the answer to one decimal place if necessary.

Accepted Answer

A)  14.5 m 
B)  331.2 m 
C)  361.9 m 
D)  72.4 m 
A)  14.5 m 
B)  331.2 m 
C)  361.9 m 
D)  72.4 m

Question 5

Evaluate the integral.
-  dx

Accepted Answer

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

Question 6

Evaluate the integral.
-

Accepted Answer

A)  -     + C 
B)  -     + C 
C)  2   + C 
D)  -     + C 
A)  -     + C 
B)  -     + C 
C)  2   + C 
D)  -     + C

Question 7

Evaluate the integral.
-    4x dx

Accepted Answer

A)  e 
B)  -   
C)    
D)  4e 
A)  e 
B)  -   
C)    
D)  4e

Question 8

Determine the indefinite integral.
-

Accepted Answer

A)        + C 
B)      + C 
C)  -       + C 
D)  -       + C 
A)        + C 
B)      + C 
C)  -       + C 
D)  -       + C

Question 9

Evaluate the definite integral.
-

Accepted Answer

A)  -14 
B)    
C)  14   
D)  28   
A)  -14 
B)    
C)  14   
D)  28

Question 10

Solve the problem.
-A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y represents the amount of the isotope left then the equation for the situation is   In how many years will there be 90% of the isotope left?

Accepted Answer

A)  527 years 
B)  1000 years 
C)  500 years 
D)  246 years 
A)  527 years 
B)  1000 years 
C)  500 years 
D)  246 years

Question 11

Solve the problem.
-Find the volume interior to the inverted catenary kiln (an oven used to fire pottery) shown in the figure. Give an exact answer in terms of logarithms.

Accepted Answer

A)  22(3 ln(3 +   ) +   ) 
B)  22(3 ln(3 +   ) -   ) 
C)  11(3 ln(3 +   ) -   ) 
D)  66 ln(3 +   ) -   
A)  22(3 ln(3 +   ) +   ) 
B)  22(3 ln(3 +   ) -   ) 
C)  11(3 ln(3 +   ) -   ) 
D)  66 ln(3 +   ) -

Question 12

Evaluate the definite integral.
-

Accepted Answer

A)  ln   
B)    
C)  ln 2 
D)  ln   
A)  ln   
B)    
C)  ln 2 
D)  ln

Question 13

Solve the problem.
-In a chemical reaction, the rate at which the amount of a reactant changes with time is proportional to the amount present, such that   , when t is measured in hours. If there are   of reactant present when t = 0, how many grams will be left after   ? Give your answer to the nearest tenth of a gram.

Accepted Answer

A)  3.7 g 
B)  11 g 
C)  7.3 g 
D)  0.1 g 
A)  3.7 g 
B)  11 g 
C)  7.3 g 
D)  0.1 g

Question 14

Write the word or phrase that best completes each statement or answers the question.  
-Derive the formula given that d/dx (cosh x) = sinh x and d/dx (sinh x) = cosh x. d/dx (coth x) = -   x

Accepted Answer

The answer of Write the word or phrase that best...

Question 15

Find the value of the x-coordinate of the points at which the functions intersect, and approximate the area of the region described. Round to two decimal places when necessary.
-f(x) = sinh x, g(x) = tanh x; the region bounded by the graphs of f, g, and ln 5

Accepted Answer

A)  x = 0; 0.54 
B)  x = 0; 0.22 
C)  x = 0; 1 
D)  x = 0; 0.64 
A)  x = 0; 0.54 
B)  x = 0; 0.22 
C)  x = 0; 1 
D)  x = 0; 0.64

Question 16

Evaluate the definite integral. Express the answer in terms of natural logarithms.
-

Accepted Answer

A)  ln(   + 3) 
B)  ln(   +   ) 
C)  ln(   + 2) 
D)  ln   
A)  ln(   + 3) 
B)  ln(   +   ) 
C)  ln(   + 2) 
D)  ln

Question 17

Evaluate the derivative.
-f(x) = 9   (cos x)

Accepted Answer

A)  -   
B)  ln   sin x 
C)  -   
D)  -   
A)  -   
B)  ln   sin x 
C)  -   
D)  -

Question 18

Evaluate the integral.
-

Accepted Answer

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

Question 19

Evaluate the definite integral.
-  (Give an approximate answer rounded to two decimal places if necessary.)

Accepted Answer

A)  1 
B)  0.71 
C)  0.73 
D)  0.75 
A)  1 
B)  0.71 
C)  0.73 
D)  0.75

Question 20

Use a calculator to evaluate the expression, or state that the value does not exist. Round the answer to four decimal places when necessary.
-csch x

Accepted Answer

A)  -2.9085 
B)  -1.571 
C)  0.0371 
D)  -0.9103 
A)  -2.9085 
B)  -1.571 
C)  0.0371 
D)  -0.9103

Evaluate the integral. - dx

Evaluate the definite integral. -

Determine the indefinite integral. - , x < ln 4

Evaluate the integral. - dx

Evaluate the integral. -

Evaluate the integral. - 4x dx

Determine the indefinite integral. -

Evaluate the definite integral. -

Solve the problem. -A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y represents the amount of the isotope left then the equation for the situation is In how many years will there be 90% of the isotope left?

Solve the problem. -Find the volume interior to the inverted catenary kiln (an oven used to fire pottery) shown in the figure. Give an exact answer in terms of logarithms.

Evaluate the definite integral. -

Write the word or phrase that best completes each statement or answers the question. -Derive the formula given that d/dx (cosh x) = sinh x and d/dx (sinh x) = cosh x. d/dx (coth x) = - x

Find the value of the x-coordinate of the points at which the functions intersect, and approximate the area of the region described. Round to two decimal places when necessary. -f(x) = sinh x, g(x) = tanh x; the region bounded by the graphs of f, g, and ln 5

Evaluate the definite integral. Express the answer in terms of natural logarithms. -

Evaluate the derivative. -f(x) = 9 (cos x)

Evaluate the integral. -

Evaluate the definite integral. - (Give an approximate answer rounded to two decimal places if necessary.)

Use a calculator to evaluate the expression, or state that the value does not exist. Round the answer to four decimal places when necessary. -csch x

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 7: Logarithmic, Exponential, and Hyperbolic Functions

Evaluate the integral. - dx

Evaluate the definite integral. -

Determine the indefinite integral. - , x < ln 4

Evaluate the integral. - dx

Evaluate the integral. -

Evaluate the integral. - 4x dx

Determine the indefinite integral. -

Evaluate the definite integral. -

Solve the problem. -A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y represents the amount of the isotope left then the equation for the situation is In how many years will there be 90% of the isotope left?

Solve the problem. -Find the volume interior to the inverted catenary kiln (an oven used to fire pottery) shown in the figure. Give an exact answer in terms of logarithms.

Evaluate the definite integral. -

Write the word or phrase that best completes each statement or answers the question. -Derive the formula given that d/dx (cosh x) = sinh x and d/dx (sinh x) = cosh x. d/dx (coth x) = - x

Find the value of the x-coordinate of the points at which the functions intersect, and approximate the area of the region described. Round to two decimal places when necessary. -f(x) = sinh x, g(x) = tanh x; the region bounded by the graphs of f, g, and ln 5

Evaluate the definite integral. Express the answer in terms of natural logarithms. -

Evaluate the derivative. -f(x) = 9 (cos x)

Evaluate the integral. -

Evaluate the definite integral. - (Give an approximate answer rounded to two decimal places if necessary.)

Use a calculator to evaluate the expression, or state that the value does not exist. Round the answer to four decimal places when necessary. -csch x

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters