# 4-11f-test3

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School
Course
Professor EGR 265, TEST III 1
EGR 265, Math Tools for Engineering Problem Solving
November 30, 2011, 50 minutes
Name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
TEST III
Problem 1 (9+9 points)
(a) Let f(x, y) = 2x
xy. Find fxx +fyy.
(b) For the function g(x, y) = xln(x2+y) ﬁnd gx,gyand gxy.
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Problem 2 (9+9 points)
(a) For the function h(x, y) = e(x4+y2)ﬁnd its direction and rate of steepest descent at
the point P(1,2).
(b) Find the directional derivative of h(x, y) at P(1,2) in the direction of the vector
from P(1,2) to Q(4,2).
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Problem 3 (12+6 points)
(a) Find an equation for the tangent plane to the graph of z=xy + cos(xy) + 1 at
the point (π
2,0,1).
(b) Also, ﬁnd parametric equations for the normal line to the graph of z=xy +cos(x
y) + 1 at (π
2,0,1).
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