Question 1

Let f(x,y) =   where k is a constant real number. Find all values of k so that the function f is continuousat (0, 0).

Accepted Answer

A)  -   or   
B)  k    R 
C)  -1 or 2 
D)  1 or -2 
E)    or -   
A)  -   or   
B)  k    R 
C)  -1 or 2 
D)  1 or -2 
E)    or -

Question 2

Find   if z =   .

Accepted Answer

A)  x(x - 1)   
B)  x   ln(x) 
C)  x   ln(y) 
D)    (1 + xln(y)) 
E)    (1 + xln(x - 1)) 
A)  x(x - 1)   
B)  x   ln(x) 
C)  x   ln(y) 
D)    (1 + xln(y)) 
E)    (1 + xln(x - 1))

Question 3

Find the Maclaurin polynomial of degree 3 for the function f(x, y) = ln(1 + x   ) and use it to find an approximate value for ln(1 + 0.1   ). State your answer to 5 decimal places.

Accepted Answer

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

Question 4

Calculate the directional derivative of the function   at (1, 1, 1) in the direction from (1, 1, 1) toward the point (-1, -2, 3).

Accepted Answer

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

Let f(x,y) = where k is a constant real number. Find all values of k so that the function f is continuousat (0, 0).

Find if z = .

Find the Maclaurin polynomial of degree 3 for the function f(x, y) = ln(1 + x ) and use it to find an approximate value for ln(1 + 0.1 ). State your answer to 5 decimal places.

Calculate the directional derivative of the function at (1, 1, 1) in the direction from (1, 1, 1) toward the point (-1, -2, 3).

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

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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

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

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Exam 13: Partial Differentiation