Question 1

Define   x, specify its domain and range, and calculate its derivative.

Accepted Answer

The answer of Define   x, specify its domain...

Question 2

Evaluate     .

Accepted Answer

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

Question 3

The function F(x) = ln   is an antiderivative of the function f(x) =   .

Accepted Answer

A) True 
 B)False  True

Question 4

Solve for x: tanh(x) =   .

Accepted Answer

By definition, tanh(

Question 5

Find an equation of the line tangent to the curve   -   = 2x at the point (0,1).

Accepted Answer

A)  y = 1 -   
B)  y = 1 +   
C)  y = -   
D)  y = -   
E)  y = -1 +   
A)  y = 1 -   
B)  y = 1 +   
C)  y = -   
D)  y = -   
E)  y = -1 +

Question 6

Find an equation of the line normal (that is, perpendicular) to the curve y = tanh x at the point on the curve where x = ln 2.

Accepted Answer

A)  y =   +   (x - ln 2) 
B)  y =   -   (x - ln 2) 
C)  y =   +   (x - ln 2) 
D)  y =   -   (x - ln 2) 
E)  y =   +   (x + ln 2) 
A)  y =   +   (x - ln 2) 
B)  y =   -   (x - ln 2) 
C)  y =   +   (x - ln 2) 
D)  y =   -   (x - ln 2) 
E)  y =   +   (x + ln 2)

Question 7

Solve the logarithmic equation   (   ) -   (6x - 1) = 0.

Accepted Answer

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

Question 8

The exact value of tan   is equal to

Accepted Answer

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

Question 9

Simplify the expression   (   ) -   (   ).

Accepted Answer

A)  3x - 3a 
B)  9x - 64a 
C)    
D)  3x - 4a 
E)    
A)  3x - 3a 
B)  9x - 64a 
C)    
D)  3x - 4a 
E)

Question 10

Solve the exponential equation   = 9.

Accepted Answer

A)  -2, -1 
B)  2, 1 
C)  2, -1 
D)  2, -2 
E)  none of the above 
A)  -2, -1 
B)  2, 1 
C)  2, -1 
D)  2, -2 
E)  none of the above

Question 11

For what value(s) of the constant m is the line y = mx tangent to the curve y =   ?

Accepted Answer

A)  e 
B)  1 
C)    
D)  ln 2 
E)    
A)  e 
B)  1 
C)    
D)  ln 2 
E)

Question 12

Let $\theta$ =     . Find tan $\theta$.

Accepted Answer

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

Question 13

The 2000 census recorded a population of 16.1 million in a certain country, while in 2010 the figure was 32.8 million. Assuming that the rate of population growth is proportional to the population, predict the population in the year 2015.

Accepted Answer

A)  39.8 million 
B)  46.8 million 
C)  36.8 million 
D)  41.8 million 
E)  52.8 million 
A)  39.8 million 
B)  46.8 million 
C)  36.8 million 
D)  41.8 million 
E)  52.8 million

Question 14

Let f(x) = (2x + 1)(3x + 1)(4x + 1)(5x + 1)(6x + 1). Use logarithmic differentiation to calculate   (0).

Accepted Answer

A)  20 
B)  1 
C)  10 
D)  40 
E)  5 
A)  20 
B)  1 
C)  10 
D)  40 
E)  5

Question 15

If sinh(x) = -   , then tanh(x) = ±

Accepted Answer

A) True 
 B)False

Question 16

Find the inverse of the function f(x) = 3   + 7.

Accepted Answer

A)      - 7 
B)    
C)    
D)  3   - 7 
E)    
A)      - 7 
B)    
C)    
D)  3   - 7 
E)

Question 17

If y = arcsin(x) + arccos(x), find   .

Accepted Answer

A)  0 
B)  arc   
C)  arccos(x) - arcsin(x) 
D)    +   
E)  -csc(x)cot(x) + sec(x)tan(x) 
A)  0 
B)  arc   
C)  arccos(x) - arcsin(x) 
D)    +   
E)  -csc(x)cot(x) + sec(x)tan(x)

Question 18

Evaluate the derivative of       at x = 3.

Accepted Answer

A)  6     -   
B)  6     +   
C)  2     - 1 
D)  3     -   
E)  6     -   
A)  6     -   
B)  6     +   
C)  2     - 1 
D)  3     -   
E)  6     -

Question 19

Find the derivative of sech(   ).

Accepted Answer

A)  -2x tanh(   ) sech(   ) 
B)  2x tanh(   ) sech(   ) 
C)  -2x   
D)  x tanh(   ) 
E)  -tanh(   ) sech(   ) 
A)  -2x tanh(   ) sech(   ) 
B)  2x tanh(   ) sech(   ) 
C)  -2x   
D)  x tanh(   ) 
E)  -tanh(   ) sech(   )

Question 20

Solve the equation   - 2   = 1 for x.

Accepted Answer

A)  -ln 2 
B)  ln 4 
C)  ln 2 
D)  1 
E)  0 
A)  -ln 2 
B)  ln 4 
C)  ln 2 
D)  1 
E)  0

Define x, specify its domain and range, and calculate its derivative.

Evaluate .

The function F(x) = ln is an antiderivative of the function f(x) = .

Solve for x: tanh(x) = .

Find an equation of the line tangent to the curve - = 2x at the point (0,1).

Find an equation of the line normal (that is, perpendicular) to the curve y = tanh x at the point on the curve where x = ln 2.

Solve the logarithmic equation ( ) - (6x - 1) = 0.

The exact value of tan is equal to

Simplify the expression ( ) - ( ).

Solve the exponential equation = 9.

For what value(s) of the constant m is the line y = mx tangent to the curve y = ?

Let $\theta$ = $Let \theta = . Find tan \theta .$ $Let \theta = . Find tan \theta .$ . Find tan $\theta$ .

The 2000 census recorded a population of 16.1 million in a certain country, while in 2010 the figure was 32.8 million. Assuming that the rate of population growth is proportional to the population, predict the population in the year 2015.

Let f(x) = (2x + 1)(3x + 1)(4x + 1)(5x + 1)(6x + 1). Use logarithmic differentiation to calculate (0).

If sinh(x) = - , then tanh(x) = ±

Find the inverse of the function f(x) = 3 + 7.

If y = arcsin(x) + arccos(x), find .

Evaluate the derivative of at x = 3.

Find the derivative of sech( ).

Solve the equation - 2 = 1 for x.

Preliminaries

Limits and Continuity

Differentiation

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 4: Transcendental Functions

Define x, specify its domain and range, and calculate its derivative.

Evaluate .

The function F(x) = ln is an antiderivative of the function f(x) = .

Solve for x: tanh(x) = .

Find an equation of the line tangent to the curve - = 2x at the point (0,1).

Find an equation of the line normal (that is, perpendicular) to the curve y = tanh x at the point on the curve where x = ln 2.

Solve the logarithmic equation ( ) - (6x - 1) = 0.

The exact value of tan is equal to

Simplify the expression ( ) - ( ).

Solve the exponential equation = 9.

For what value(s) of the constant m is the line y = mx tangent to the curve y = ?

Let θ\thetaθ = . Find tan θ\thetaθ .

The 2000 census recorded a population of 16.1 million in a certain country, while in 2010 the figure was 32.8 million. Assuming that the rate of population growth is proportional to the population, predict the population in the year 2015.

Let f(x) = (2x + 1)(3x + 1)(4x + 1)(5x + 1)(6x + 1). Use logarithmic differentiation to calculate (0).

If sinh(x) = - , then tanh(x) = ±

Find the inverse of the function f(x) = 3 + 7.

If y = arcsin(x) + arccos(x), find .

Evaluate the derivative of at x = 3.

Find the derivative of sech( ).

Solve the equation - 2 = 1 for x.

Preliminaries

Limits and Continuity

Differentiation

More Applications of Differentiation

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Let $\theta$ = $Let \theta = . Find tan \theta .$ $Let \theta = . Find tan \theta .$ . Find tan $\theta$ .