Calculus 3 Exam 2
3
2
5. Given f ( x , y ) =x y + x y .
a) Find a vector that points in the direction where the directional derivative of
f
at (-1,1)
has a maximum.
b) What is the maximum value of the
Calculus 3 Exam 2
1. Consider the function f ( x , y ) = x 1
a) Sketch the domain of f
b) Identify the range of f
in
R2 .
in .
c) Sketch (and describe as needed) the graph of f
2. Consider
z= yx
2
.
a
Calculus 3 Exam 2
1. Consider the function f ( x , y ) = x 1
a) Sketch the domain of f
b) Identify the range of f
in
R2 .
in .
c) Sketch (and describe as needed) the graph of f
2. Consider
z= yx 2 .
a
Calculus 3 Exam 2
3. Consider each limit that follows.
2
2
2
x y z
a) Evaluate the limit (x , y , z) (1,1,1) x 2 y 2xyz
lim
x2 + y2
b) Show the limit (x , y)(0,0 ) x + y 2
lim
does not exist
3
2
4. Fi
Calculus 3 Exam 2
2 3
7. Find the equation of the plane tangent to the graph of f ( x , y ) =x y at (2,1).
2
8. Given f ( x , y ) =x y
3
.
1 3
a) Find the directional derivative at (2,1) in the direct
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