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This is the Exam of Multivariable Calculus and its key important points are: Function, Two Independent Variable, Direction, Derivative, Equation, Tangent Plane, Linear Approximation, Approximate Value, Critical Point, Average Value
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MA 174: Multivariable Calculus
Mar. 23, 2007
NO CALCULATORS, BOOKS, OR PAPERS ARE ALLOWED. Use the back
of the test pages for scrap paper.
Points awarded
Total Points: / 45
2
and z, find
∂x
∂z
at (x, y, z) = (1, − 1 , −3).
1
6
1
5
1
3
1
2
2
1
2
y
2
at (− 1 , −1) equal to
zero.
A. 3 i
i + 2
j −
k
i − 5
j
i + 5
j
2
1
2
y
2 at (− 1 , −1).
A. 5 x + 2y + z −
7
2
B. 5 x + 2y − z −
7
2
C. 5 x − 2 y + z −
7
2
D. 5 x − 2 y − z +
7
2
E. 5 x + 2y + z +
7
2
0 ≤ y ≤ π.
B. π
2
π
D. 2 π
sphere x
2
2
2
= 1 are ,.
Answer:
w = z − x, write
∂f
∂x
in terms of
∂f
∂u
∂f
∂v
and
∂f
∂w
∂f
∂x
and then compute
∂f
∂x
∂f
∂y
∂f
∂z
Answer:
∂f
∂u
∂f
∂w
