Question 1

If f(x) =   , calculate f'(-2) directly from the definition of the derivative.

Accepted Answer

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

Question 2

A rock is thrown upwards at 5 m/s from the top of a building 80 m high. When will it hit the ground (to the nearest tenth of a second)?

Accepted Answer

A)  4.6 s 
B)  4.1 s 
C)  3.6 s 
D)  3.1 s 
E)  5.1 s 
A)  4.6 s 
B)  4.1 s 
C)  3.6 s 
D)  3.1 s 
E)  5.1 s A

Question 3

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

Accepted Answer

A)  2x + y - 4 = 0 
B)  2x + y + 4 = 0 
C)  2x - y - 4 = 0 
D)  2x - y + 4 = 0 
E)  2x + y = 0 
A)  2x + y - 4 = 0 
B)  2x + y + 4 = 0 
C)  2x - y - 4 = 0 
D)  2x - y + 4 = 0 
E)  2x + y = 0 A

Question 4

Find an equation of the line tangent to the curve y =   at the point where x = 2.

Accepted Answer

A)  y = -4x + 12 
B)  y = 4x - 4 
C)  y = -4x + 4 
D)  y = 4x + 4 
E)  y = 4x - 12 
A)  y = -4x + 12 
B)  y = 4x - 4 
C)  y = -4x + 4 
D)  y = 4x + 4 
E)  y = 4x - 12

Question 5

If the line 4x - 9y = 0 is tangent in the first quadrant to the graph of y =     + c, what is the value of c?

Accepted Answer

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

Question 6

Find the derivative of f(x) =   .

Accepted Answer

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

Question 7

Find an equation of the line tangent to the curve y = 2x -   at the point where x = 2.

Accepted Answer

A)  25y = 49x - 1 
B)  5y = 49x + 1 
C)  25y = 49x + 1 
D)  25y = 41x + 1 
E)  25x = 49y + 1 
A)  25y = 49x - 1 
B)  5y = 49x + 1 
C)  25y = 49x + 1 
D)  25y = 41x + 1 
E)  25x = 49y + 1

Question 8

Calculate the third derivative of f(x) =   x.

Accepted Answer

A)  -2sin(2x) 
B)  -4sin(2x) 
C)  -2cos(2x) 
D)  -4sin x 
E)  -2(x)   
A)  -2sin(2x) 
B)  -4sin(2x) 
C)  -2cos(2x) 
D)  -4sin x 
E)  -2(x)

Question 9

If     exists, then f is continuous at x = a.

Accepted Answer

A) True 
 B)False

Question 10

Find the solution of the differential equation   =     such that y = 85 whenx = 8.

Accepted Answer

A)  y = 7   -     +   - 1 
B)  y = 7   -     +   + 1 
C)  y = 7   -     +     + 63 
D)  y = -7   +     -   + 171 
E)  none of the above 
A)  y = 7   -     +   - 1 
B)  y = 7   -     +   + 1 
C)  y = 7   -     +     + 63 
D)  y = -7   +     -   + 171 
E)  none of the above

Question 11

Evaluate   dx.

Accepted Answer

A)      + C 
B)  3   + C 
C)  4x + C 
D)      + C 
E)  x + C 
A)      + C 
B)  3   + C 
C)  4x + C 
D)      + C 
E)  x + C

Question 12

The population (in thousands) of the city of Abbotsford is given by   , with t in years and with   corresponding to 1980. What was the rate of change of P in 1986?

Accepted Answer

A)  9.6 thousand per year 
B)  8.6 thousand per year 
C)  7.6 thousand per year 
D)  8.9 thousand per year 
E)  4.4 thousand per year 
A)  9.6 thousand per year 
B)  8.6 thousand per year 
C)  7.6 thousand per year 
D)  8.9 thousand per year 
E)  4.4 thousand per year

Question 13

Use implicit differentiation to find   if   +   = 6xy.

Accepted Answer

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

Question 14

Determine the open intervals on the x-axis on which the function   is increasing and those on which it is decreasing.

Accepted Answer

A)  increasing on (-$\infty$, 3) and decreasing on (3, $\infty$) 
B)  increasing on (-$\infty$, 0) and decreasing on (0, $\infty$) 
C)  increasing on (0, 3) and decreasing on (-$\infty$, 0) and (3, $\infty$) 
D)  decreasing on (0, 3) and increasing on (-$\infty$, 0) and (3, $\infty$) 
E)  decreasing on (-$\infty$, 3) and increasing on (3, $\infty$) 
A)  increasing on (-$\infty$, 3) and decreasing on (3, $\infty$) 
B)  increasing on (-$\infty$, 0) and decreasing on (0, $\infty$) 
C)  increasing on (0, 3) and decreasing on (-$\infty$, 0) and (3, $\infty$) 
D)  decreasing on (0, 3) and increasing on (-$\infty$, 0) and (3, $\infty$) 
E)  decreasing on (-$\infty$, 3) and increasing on (3, $\infty$)

Question 15

Find an equation of the line tangent to the curve y =   at the point (1, 3).

Accepted Answer

A)  y = -   x +   
B)  y = -   x -   
C)  y =   x +   
D)  y =   x -   
E)  y = 3x - 10 
A)  y = -   x +   
B)  y = -   x -   
C)  y =   x +   
D)  y =   x -   
E)  y = 3x - 10

Question 16

(x) = -cos(4x) + 34,   (x) = 2   (2x) - 15, and   (x) = 7 -2   (2x) are all antiderivatives of f(x) = 8 sin(2x) cos(2x).

Accepted Answer

A) True 
 B)False

Question 17

Where does the function f(x) =   fail to be differentiable?

Accepted Answer

A)  f(x) is differentiable everywhere. 
B)  at x = 0 
C)  at x = 1 
D)  at x = 0 and x = 1 
E)  none of the above 
A)  f(x) is differentiable everywhere. 
B)  at x = 0 
C)  at x = 1 
D)  at x = 0 and x = 1 
E)  none of the above

Question 18

Find an equation of the line tangent to the curve y =   + 1 at the point where x = 2.

Accepted Answer

A)  y = 12x + 15 
B)  y = 12x -15 
C)  y = -12x -15 
D)  y = -12x + 15 
E)  y = 15x + 12 
A)  y = 12x + 15 
B)  y = 12x -15 
C)  y = -12x -15 
D)  y = -12x + 15 
E)  y = 15x + 12

Question 19

If f'(x) = 0 at every point of the domain of f, then f is constant on its domain.

Accepted Answer

A) True 
 B)False

Question 20

Find     . Simplify your answer.

Accepted Answer

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

If f(x) = , calculate f'(-2) directly from the definition of the derivative.

A rock is thrown upwards at 5 m/s from the top of a building 80 m high. When will it hit the ground (to the nearest tenth of a second)?

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

Find an equation of the line tangent to the curve y = at the point where x = 2.

If the line 4x - 9y = 0 is tangent in the first quadrant to the graph of y = + c, what is the value of c?

Find the derivative of f(x) = .

Find an equation of the line tangent to the curve y = 2x - at the point where x = 2.

Calculate the third derivative of f(x) = x.

If exists, then f is continuous at x = a.

Find the solution of the differential equation = such that y = 85 whenx = 8.

Evaluate dx.

The population (in thousands) of the city of Abbotsford is given by , with t in years and with corresponding to 1980. What was the rate of change of P in 1986?

Use implicit differentiation to find if + = 6xy.

Determine the open intervals on the x-axis on which the function is increasing and those on which it is decreasing.

Find an equation of the line tangent to the curve y = at the point (1, 3).

(x) = -cos(4x) + 34, (x) = 2 (2x) - 15, and (x) = 7 -2 (2x) are all antiderivatives of f(x) = 8 sin(2x) cos(2x).

Where does the function f(x) = fail to be differentiable?

Find an equation of the line tangent to the curve y = + 1 at the point where x = 2.

If f'(x) = 0 at every point of the domain of f, then f is constant on its domain.

Find . Simplify your answer.

Preliminaries

Limits and Continuity

Transcendental Functions

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

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Exam 3: Differentiation

If f(x) = , calculate f'(-2) directly from the definition of the derivative.

A rock is thrown upwards at 5 m/s from the top of a building 80 m high. When will it hit the ground (to the nearest tenth of a second)?

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

Find an equation of the line tangent to the curve y = at the point where x = 2.

If the line 4x - 9y = 0 is tangent in the first quadrant to the graph of y = + c, what is the value of c?

Find the derivative of f(x) = .

Find an equation of the line tangent to the curve y = 2x - at the point where x = 2.

Calculate the third derivative of f(x) = x.

If exists, then f is continuous at x = a.

Find the solution of the differential equation = such that y = 85 whenx = 8.

Evaluate dx.

The population (in thousands) of the city of Abbotsford is given by , with t in years and with corresponding to 1980. What was the rate of change of P in 1986?

Use implicit differentiation to find if + = 6xy.

Determine the open intervals on the x-axis on which the function is increasing and those on which it is decreasing.

Find an equation of the line tangent to the curve y = at the point (1, 3).

(x) = -cos(4x) + 34, (x) = 2 (2x) - 15, and (x) = 7 -2 (2x) are all antiderivatives of f(x) = 8 sin(2x) cos(2x).

Where does the function f(x) = fail to be differentiable?

Find an equation of the line tangent to the curve y = + 1 at the point where x = 2.

If f'(x) = 0 at every point of the domain of f, then f is constant on its domain.

Find . Simplify your answer.

Preliminaries

Limits and Continuity

Transcendental Functions

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