Question 1

Evaluate .

Accepted Answer

A)  $\infty$ 
B)  1 
C)  0 
D)  -$\infty$ 
E)  2 
A)  $\infty$ 
B)  1 
C)  0 
D)  -$\infty$ 
E)  2

Question 2

Evaluate .

Accepted Answer

A)  -   
B)  -2 
C)  1 
D)    
E)    
A)  -   
B)  -2 
C)  1 
D)    
E)

Question 3

Let f(x) =   . Find   f(x).

Accepted Answer

A)  +$\infty$ 
B)  0 
C)  1 
D)  -$\infty$ 
E)  -1 
A)  +$\infty$ 
B)  0 
C)  1 
D)  -$\infty$ 
E)  -1

Question 4

Evaluate .

Accepted Answer

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

Question 5

Let g(x) =   .Evaluate   g(x).

Accepted Answer

A)  $\infty$ 
B)  -3 
C)  -$\infty$ 
D)  1 
E)  none of the above 
A)  $\infty$ 
B)  -3 
C)  -$\infty$ 
D)  1 
E)  none of the above

Question 6

Evaluate .

Accepted Answer

A)  -3 
B)  3 
C)  1 
D)  -1 
E)  does not exist 
A)  -3 
B)  3 
C)  1 
D)  -1 
E)  does not exist

Question 7

Evaluate .

Accepted Answer

A)  $\infty$ 
B)  -$\infty$ 
C)  0 
D)  -1 
E)  -2 
A)  $\infty$ 
B)  -$\infty$ 
C)  0 
D)  -1 
E)  -2

Question 8

Evaluate .

Accepted Answer

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

Question 9

If     = -32, find k.

Accepted Answer

The answer of If     = -32,...

Question 10

An object moves along the x-axis so that its velocity at time t seconds is v(t) =   m/s. What is the average acceleration (i.e., average rate of change of the velocity) of the object over the time interval[2, 2 + h]? What is the acceleration of the object at time t = 2s?

Accepted Answer

A)  -   m/   , -   m/   
B)    m/   ,   m/   
C)    m/   ,   m/   
D)  -   m/   , -   m/   
E)    m/   ,   m/   
A)  -   m/   , -   m/   
B)    m/   ,   m/   
C)    m/   ,   m/   
D)  -   m/   , -   m/   
E)    m/   ,   m/

Question 11

An object moves along the x-axis so that at time t seconds (where t $\ge$0) it is x =   m to the right of the origin. By calculating the average velocity of the object over time intervals [4, 4 + h] for h = 0.1, h = 0.01, h = 0.001, and h = 0.0001, determine the velocity of the particle at time t = 4s.

Accepted Answer

A)  0.2499 m/s 
B)  0.2498 m/s 
C)  0.2485 m/s 
D)  0.2000 m/s 
E)  0.2501 m/s 
A)  0.2499 m/s 
B)  0.2498 m/s 
C)  0.2485 m/s 
D)  0.2000 m/s 
E)  0.2501 m/s

Question 12

Evaluate the following limit:   x   .

Accepted Answer

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

Question 13

Given f(x) = 4x + 7 and a number   > 0, find the largest value of   for which 0 <   <   will imply that   .

Accepted Answer

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

Question 14

The polynomial function P(x) =   +   - 7   - 2x + 10 has a zero in the closed interval [1 , 2].

Accepted Answer

A) True 
 B)False

Question 15

Evaluate the following limits:
(i)     
(ii)

Accepted Answer

A)  (i)   (ii) -6 
B)  (i)   (ii) 6 
C)  (i) 1 (ii) 1 
D)  (i)   (ii) does not exist 
E)  (i)   (ii) does not exist 
A)  (i)   (ii) -6 
B)  (i)   (ii) 6 
C)  (i) 1 (ii) 1 
D)  (i)   (ii) does not exist 
E)  (i)   (ii) does not exist

Question 16

Evaluate .

Accepted Answer

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

Question 17

Evaluate .

Accepted Answer

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

Question 18

Accepted Answer

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

Question 19

Evaluate .

Accepted Answer

A)    
B)  2   
C)    
D)  4 
E)  does not exist 
A)    
B)  2   
C)    
D)  4 
E)  does not exist

Question 20

Complete the following definition: We say   f(x) = L if for every   > 0 there exists   > 0 depending on   such that

Accepted Answer

A)  if a -   < x < a, then |f(x) - L| <   
B)  if |x - a| <  , then |f(x) - L| <  
C)  if |x - a| <  , then f(x) - L <   
D)  if a < x < a +  , then |f(x) - L| <   
E)  none of the above 
A)  if a -   < x < a, then |f(x) - L| <   
B)  if |x - a| <  , then |f(x) - L| <  
C)  if |x - a| <  , then f(x) - L <   
D)  if a < x < a +  , then |f(x) - L| <   
E)  none of the above

Evaluate .

Evaluate .

Let f(x) = . Find f(x).

Evaluate .

Let g(x) = .Evaluate g(x).

Evaluate .

Evaluate .

Evaluate .

If = -32, find k.

An object moves along the x-axis so that its velocity at time t seconds is v(t) = m/s. What is the average acceleration (i.e., average rate of change of the velocity) of the object over the time interval[2, 2 + h]? What is the acceleration of the object at time t = 2s?

Evaluate the following limit: x .

Given f(x) = 4x + 7 and a number > 0, find the largest value of for which 0 < < 11ee7b11_3aa8_6932_ae82_3b68ee6209d9_TB9661_11 will imply that .

The polynomial function P(x) = + - 7 - 2x + 10 has a zero in the closed interval [1 , 2].

Evaluate the following limits: (i) (ii)

Evaluate .

Evaluate .

Evaluate .

Complete the following definition: We say f(x) = L if for every > 0 there exists > 0 depending on 11ee7b11_3aa8_6932_ae82_3b68ee6209d9_TB9661_11 such that

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Exam 2: Limits and Continuity

Evaluate .

Evaluate .

Let f(x) = . Find f(x).

Evaluate .

Let g(x) = .Evaluate g(x).

Evaluate .

Evaluate .

Evaluate .

If = -32, find k.

An object moves along the x-axis so that its velocity at time t seconds is v(t) = m/s. What is the average acceleration (i.e., average rate of change of the velocity) of the object over the time interval[2, 2 + h]? What is the acceleration of the object at time t = 2s?

Evaluate the following limit: x .

Given f(x) = 4x + 7 and a number > 0, find the largest value of for which 0 < < 11ee7b11_3aa8_6932_ae82_3b68ee6209d9_TB9661_11 will imply that .

The polynomial function P(x) = + - 7 - 2x + 10 has a zero in the closed interval [1 , 2].

Evaluate the following limits: (i) (ii)

Evaluate .

Evaluate .

Evaluate .

Complete the following definition: We say f(x) = L if for every > 0 there exists > 0 depending on 11ee7b11_3aa8_6932_ae82_3b68ee6209d9_TB9661_11 such that

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