EGR 265, TEST III 1

EGR 265, Math Tools for Engineering Problem Solving

April 18, 2011, 50 minutes

Name (Print last name ﬁrst): ..........................................

TEST III

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Problem 1 (9+9 points)

(a) Let f(x, y) = 2x2y2+ 3y3. Find fxx +fyy.

(b) For the function g(x, y) = xexy ﬁnd gx,gyand gyx.

EGR 265, TEST III 2

Problem 2 (9+9 points)

(a) For the function h(x, y) = ln(x2+y2) ﬁnd its direction and rate of steepest descent

at the point P(1,1).

(b) Find the directional derivative of h(x, y) at P(1,1) in the direction of the vector

v=−4i+ 3j.