Math 206 Test Two
Name:
1. (5 marks) Suppose f(x, y) = x−2y.
a. Evaluate k~
∇f(0,0)k. Show your work.
b. Evaluate D(1,−2)f(0,0). Show your work.
1
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Length - Multivariable - Exam, Exams of Mathematics
This is the Exam of Multivariable which includes Plane Consisting, Perpendicular, Parametrized, Parametric Equation, Parameter etc. Key important points are: Length, Evaluate, Path Integral, Parametrization, Curve, Double Integral, Parallelogram, Surface Integral, Plane Spanned, Vectors
Typology: Exams
2012/2013
1 / 5
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Math 206 Test Two
Name:
- (5 marks) Suppose f (x, y) = x − 2 y.
a. Evaluate ‖
∇f (0, 0)‖. Show your work.
b. Evaluate D (1,−2)
f (0, 0). Show your work.
- (5 marks) Suppose f (x, y, z) = x
2
- y
2 − 2 z
2 .
a. Evaluate div(
∇f ). Show your work.
b. Evaluate curl(
∇f ). Show your work.
- (5 marks) Suppose D is the parallelogram in the plane spanned by the
vectors (1, 1) and (1, 0).
a. Evaluate the double integral
∫ ∫
D
xydA. Show your work.
b. Find a parametrization for the parallelogram in R
3
. Show your work.
c. Evaluate the surface integral
∫ ∫
D
xydσ. Show your work.
- (5 marks) Change the order of integration in the following triple integral
to represent the integral in terms of the other two types of solids (x-simple
and y-simple.)
∫ 2
0
∫ 4 − 2 x
0
∫ 8 − 4 x− 2 y
0
f (x, y, z)dzdydx.
Show your work.