Question 1

Use l'H   pital's Rule to evaluate the limit.
-

Accepted Answer

A)  $\infty$ 
B)  1 
C)  0 
D)    
A)  $\infty$ 
B)  1 
C)  0 
D)

Question 2

Find the derivative of y with respect to x, t, or θ, as appropriate
-y = ln(cos(ln $\theta$)

Accepted Answer

A)  -tan(ln $\theta$) 
B)  tan(ln$\theta$) 
C)    
D)  -   
A)  -tan(ln $\theta$) 
B)  tan(ln$\theta$) 
C)    
D)  -

Question 3

Evaluate the integral.
-  dt

Accepted Answer

A)    -   
B)  2 ln 6 
C)  12 
D)  6 
A)    -   
B)  2 ln 6 
C)  12 
D)  6

Question 4

Solve the problem.
-The barometric pressure p at an altitude of h miles above sea level satisfies the differential equation   If the pressure at sea level is 29.92 inches of mercury, find the barometric pressure at 22,000 ft.

Accepted Answer

A)  6.5 in. 
B)  68.85 in. 
C)  13 in. 
D)  0.37 in. 
A)  6.5 in. 
B)  68.85 in. 
C)  13 in. 
D)  0.37 in.

Question 5

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible.
-coth(ln 9)

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Solve the problem.
-The charcoal from a tree killed in a volcanic eruption contained 64.7% of the   found in living matter. How old is the tree, to the nearest year? Use   for the half-life of

Accepted Answer

A)  1720 years 
B)  5700 years 
C)  3581 years 
D)  2482 years 
A)  1720 years 
B)  5700 years 
C)  3581 years 
D)  2482 years

Question 8

Write the word or phrase that best completes each statement or answers the question.  
-Verify the identity. cosh(   x) =   , for all x

Accepted Answer

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

Question 9

Evaluate the integral.
-  sin t dt

Accepted Answer

A)    
B)    
C)    
D)  3 
A)    
B)    
C)    
D)  3

Question 10

Evaluate the derivative.
-f(t) = 5

Accepted Answer

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

Question 11

Determine the indefinite integral.
-    (Simplify the answer using the definitions of hyperbolic functions.)

Accepted Answer

A)    + C 
B)  x +   + C 
C)    + C 
D)  cosh x + C 
A)    + C 
B)  x +   + C 
C)    + C 
D)  cosh x + C

Question 12

Evaluate the integral.
-

Accepted Answer

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

Question 13

Evaluate the integral.
-

Accepted Answer

A)  6 sin x + C 
B)  6 ln   + C 
C)  ln   + C 
D)    ln   + C 
A)  6 sin x + C 
B)  6 ln   + C 
C)  ln   + C 
D)    ln   + C

Question 14

Solve the problem.
-A loaf of bread is removed from an oven at   and cooled in a room whose temperature is   . If the bread cools to   in 20 minutes, how much longer will it take the bread to cool to

Accepted Answer

A)  17 min 
B)  4 min 
C)  24 min 
D)  5 min 
A)  17 min 
B)  4 min 
C)  24 min 
D)  5 min

Question 15

Write the word or phrase that best completes each statement or answers the question.  
-Verify the identity using the definitions of hyperbolic functions. coth (-x) = -coth x

Accepted Answer

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

Question 16

Evaluate the derivative.
-f(x) =   ( 6/x)

Accepted Answer

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

Question 17

Evaluate the integral.
-

Accepted Answer

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

Question 18

Evaluate the integral.
-  dx

Accepted Answer

A)  21 
B)    
C)    
D)    
A)  21 
B)    
C)    
D)

Question 19

Evaluate the integral.
-

Accepted Answer

A)  2 ln 2 
B)  2 ln 3 
C)  4 ln 2 
D)  -2 ln 2 
A)  2 ln 2 
B)  2 ln 3 
C)  4 ln 2 
D)  -2 ln 2

Question 20

Write the word or phrase that best completes each statement or answers the question.  
-Verify the identity using the definitions of hyperbolic functions. coth x =

Accepted Answer

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

Use l'H pital's Rule to evaluate the limit. -

Find the derivative of y with respect to x, t, or θ, as appropriate -y = ln(cos(ln $\theta$ )

Evaluate the integral. - dt

Solve the problem. -The barometric pressure p at an altitude of h miles above sea level satisfies the differential equation If the pressure at sea level is 29.92 inches of mercury, find the barometric pressure at 22,000 ft.

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible. -coth(ln 9)

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

Solve the problem. -The charcoal from a tree killed in a volcanic eruption contained 64.7% of the found in living matter. How old is the tree, to the nearest year? Use for the half-life of

Write the word or phrase that best completes each statement or answers the question. -Verify the identity. cosh( x) = , for all x

Evaluate the integral. - sin t dt

Evaluate the derivative. -f(t) = 5

Determine the indefinite integral. - (Simplify the answer using the definitions of hyperbolic functions.)

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -A loaf of bread is removed from an oven at and cooled in a room whose temperature is . If the bread cools to in 20 minutes, how much longer will it take the bread to cool to

Write the word or phrase that best completes each statement or answers the question. -Verify the identity using the definitions of hyperbolic functions. coth (-x) = -coth x

Evaluate the derivative. -f(x) = ( 6/x)

Evaluate the integral. -

Evaluate the integral. - dx

Evaluate the integral. -

Write the word or phrase that best completes each statement or answers the question. -Verify the identity using the definitions of hyperbolic functions. coth 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

Use l'H pital's Rule to evaluate the limit. -

Find the derivative of y with respect to x, t, or θ, as appropriate -y = ln(cos(ln θ\thetaθ )

Evaluate the integral. - dt

Solve the problem. -The barometric pressure p at an altitude of h miles above sea level satisfies the differential equation If the pressure at sea level is 29.92 inches of mercury, find the barometric pressure at 22,000 ft.

Evaluate the expression without using a calculator, or state that the value does not exist. Simplify the answer to the extent possible. -coth(ln 9)

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

Solve the problem. -The charcoal from a tree killed in a volcanic eruption contained 64.7% of the found in living matter. How old is the tree, to the nearest year? Use for the half-life of

Write the word or phrase that best completes each statement or answers the question. -Verify the identity. cosh( x) = , for all x

Evaluate the integral. - sin t dt

Evaluate the derivative. -f(t) = 5

Determine the indefinite integral. - (Simplify the answer using the definitions of hyperbolic functions.)

Evaluate the integral. -

Evaluate the integral. -

Solve the problem. -A loaf of bread is removed from an oven at and cooled in a room whose temperature is . If the bread cools to in 20 minutes, how much longer will it take the bread to cool to

Write the word or phrase that best completes each statement or answers the question. -Verify the identity using the definitions of hyperbolic functions. coth (-x) = -coth x

Evaluate the derivative. -f(x) = ( 6/x)

Evaluate the integral. -

Evaluate the integral. - dx

Evaluate the integral. -

Write the word or phrase that best completes each statement or answers the question. -Verify the identity using the definitions of hyperbolic functions. coth 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

Find the derivative of y with respect to x, t, or θ, as appropriate -y = ln(cos(ln $\theta$ )