Question 1

Find .

Accepted Answer

A)  0 
B)  $\infty$ 
C)    
D)  2 
E)  does not exist 
A)  0 
B)  $\infty$ 
C)    
D)  2 
E)  does not exist

Question 2

Evaluate .

Accepted Answer

A)  -1 
B)  -2 
C)  1 
D)  0 
E)  does not exist 
A)  -1 
B)  -2 
C)  1 
D)  0 
E)  does not exist

Question 3

Which of the following conditions will guarantee that   <   ?

Accepted Answer

A)  -   < x - 2 <   
B)  |x - 2| <   
C)  |x - 2| <   
D)  all of the above 
E)  none of the above 
A)  -   < x - 2 <   
B)  |x - 2| <   
C)  |x - 2| <   
D)  all of the above 
E)  none of the above

Question 4

Evaluate .

Accepted Answer

A)    
B)  0 
C)    
D)  -   
E)  does not exist 
A)    
B)  0 
C)    
D)  -   
E)  does not exist

Question 5

Evaluate .

Accepted Answer

A)    
B)    
C)  1 
D)    
E)  does not exist 
A)    
B)    
C)  1 
D)    
E)  does not exist

Question 6

Evaluate .

Accepted Answer

A)  - $\infty$ 
B)  -   
C)    
D)    
E)  0 
A)  - $\infty$ 
B)  -   
C)    
D)    
E)  0

Question 7

Find the limit of f(x) as x approaches 2 if f is defined byf(x) =

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  0 
E)  does not exist 
A)  1 
B)  2 
C)  3 
D)  0 
E)  does not exist

Question 8

Evaluate   (2 tan x + 3 cot x).

Accepted Answer

A)  3 
B)  2 
C)  $\infty$ 
D)  -$\infty$ 
E)  5 
A)  3 
B)  2 
C)  $\infty$ 
D)  -$\infty$ 
E)  5

Question 9

Evaluate .

Accepted Answer

A)  1 
B)  -$\infty$ 
C)  $\infty$ 
D)  0 
E)  none of the above 
A)  1 
B)  -$\infty$ 
C)  $\infty$ 
D)  0 
E)  none of the above

Question 10

Evaluate     .

Accepted Answer

A)  3 
B)  1 
C)  4 
D)  0 
E)  does not exist 
A)  3 
B)  1 
C)  4 
D)  0 
E)  does not exist

Question 11

Accepted Answer

A) True 
 B)False

Question 12

Evaluate .

Accepted Answer

A)    
B)  0 
C)    
D)  -   
E)  - $\infty$ 
A)    
B)  0 
C)    
D)  -   
E)  - $\infty$

Question 13

Find the limit.

Accepted Answer

A)  -   
B)    
C)    
D)    
E)  does not exist 
A)  -   
B)    
C)    
D)    
E)  does not exist

Question 14

Evaluate .

Accepted Answer

A)  $\infty$ 
B)  -$\infty$ 
C)  1 
D)  0 
E)  does not exist 
A)  $\infty$ 
B)  -$\infty$ 
C)  1 
D)  0 
E)  does not exist

Question 15

Accepted Answer

A) True 
 B)False

Question 16

Accepted Answer

A) True 
 B)False

Question 17

If     = - 5, find   f(x).

Accepted Answer

A)  14 
B)  - 14 
C)  0 
D)  $\infty$ 
E)  - 19 
A)  14 
B)  - 14 
C)  0 
D)  $\infty$ 
E)  - 19

Question 18

Evaluate .

Accepted Answer

A)  4/7 
B)  2/5 
C)  0 
D)  1/2 
E)  does not exist 
A)  4/7 
B)  2/5 
C)  0 
D)  1/2 
E)  does not exist

Question 19

If   f(x) exists and is finite, then either f is continuous at x = c or f has a continuous extension to x = c.

Accepted Answer

A) True 
 B)False

Question 20

Evaluate .

Accepted Answer

A) $\infty$ 
B)  -2 
C)  0 
D)  -$\infty$ 
E)   $\pi$ 
A) $\infty$ 
B)  -2 
C)  0 
D)  -$\infty$ 
E)   $\pi$

Find .

Evaluate .

Which of the following conditions will guarantee that < ?

Evaluate .

Evaluate .

Evaluate .

Find the limit of f(x) as x approaches 2 if f is defined byf(x) =

Evaluate (2 tan x + 3 cot x).

Evaluate .

Evaluate .

Evaluate .

Find the limit.

Evaluate .

If = - 5, find f(x).

Evaluate .

If f(x) exists and is finite, then either f is continuous at x = c or f has a continuous extension to x = c.

Evaluate .

Preliminaries

Differentiation

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

Exam 2: Limits and Continuity

Find .

Evaluate .

Which of the following conditions will guarantee that < ?

Evaluate .

Evaluate .

Evaluate .

Find the limit of f(x) as x approaches 2 if f is defined byf(x) =

Evaluate (2 tan x + 3 cot x).

Evaluate .

Evaluate .

Evaluate .

Find the limit.

Evaluate .

If = - 5, find f(x).

Evaluate .

If f(x) exists and is finite, then either f is continuous at x = c or f has a continuous extension to x = c.

Evaluate .

Preliminaries

Differentiation

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