Question 1

Evaluate .

Accepted Answer

A)  0 
B)  1 
C)  $\infty$ 
D)  -1 
E)  3 
A)  0 
B)  1 
C)  $\infty$ 
D)  -1 
E)  3

Question 2

A function is continuous on the interval [3, 5] and takes the values f(3) = 0 and f(5) =  $\pi$ - 2. Which of the numbers 1, 2, 3, 4, or 5 must belong to the range of f?

Accepted Answer

A)  only 1 
B)  only 4 
C)  only 1 and 2 
D)  only 3, 4, and 5 
E)  only 3 and 5 
A)  only 1 
B)  only 4 
C)  only 1 and 2 
D)  only 3, 4, and 5 
E)  only 3 and 5

Question 3

Accepted Answer

A)    =   
B)    =   
C)   =   
D)    = min{1,  } 
E)    = - 2   
A)    =   
B)    =   
C)   =   
D)    = min{1,  } 
E)    = - 2

Question 4

Evaluate .

Accepted Answer

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

Question 5

Evaluate .

Accepted Answer

A)  -1 
B)  1 
C)  4 
D)  ±1 
E)  does not exist 
A)  -1 
B)  1 
C)  4 
D)  ±1 
E)  does not exist

Question 6

Evaluate .

Accepted Answer

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

Question 7

For what value of the constant c is the function f(x) =   continuous everywhere?

Accepted Answer

A)    
B)    
C)  1 
D)  0 
E)  none of the above 
A)    
B)    
C)  1 
D)  0 
E)  none of the above

Question 8

If   f(x) = L, then =   .

Accepted Answer

A) True 
 B)False

Question 9

Evaluate .

Accepted Answer

A)  $\infty$ 
B)  -$\infty$ 
C)  2 
D)  -   
E)  none of the above 
A)  $\infty$ 
B)  -$\infty$ 
C)  2 
D)  -   
E)  none of the above

Question 10

Evaluate .

Accepted Answer

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

Question 11

If   f(x) = 0, then =     =$\infty$

Accepted Answer

A) True 
 B)False

Question 12

Accepted Answer

A) True 
 B)False

Evaluate .

A function is continuous on the interval [3, 5] and takes the values f(3) = 0 and f(5) = $\pi$ - 2. Which of the numbers 1, 2, 3, 4, or 5 must belong to the range of f?

Evaluate .

Evaluate .

Evaluate .

For what value of the constant c is the function f(x) = continuous everywhere?

If f(x) = L, then = .

Evaluate .

Evaluate .

If $If f(x) = 0, then = = \infty$ f(x) = 0, then = $If f(x) = 0, then = = \infty$ $If f(x) = 0, then = = \infty$ = $\infty$

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

Evaluate .

A function is continuous on the interval [3, 5] and takes the values f(3) = 0 and f(5) = π\piπ - 2. Which of the numbers 1, 2, 3, 4, or 5 must belong to the range of f?

Evaluate .

Evaluate .

Evaluate .

For what value of the constant c is the function f(x) = continuous everywhere?

If f(x) = L, then = .

Evaluate .

Evaluate .

If f(x) = 0, then = = ∞\infty∞

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

A function is continuous on the interval [3, 5] and takes the values f(3) = 0 and f(5) = $\pi$ - 2. Which of the numbers 1, 2, 3, 4, or 5 must belong to the range of f?

If $If f(x) = 0, then = = \infty$ f(x) = 0, then = $If f(x) = 0, then = = \infty$ $If f(x) = 0, then = = \infty$ = $\infty$