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

x−y. Find fxx +fyy.

(b) For the function g(x, y) = xln(x2+y) ﬁnd gx,gyand gxy.

EGR 265, TEST III 2

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).

EGR 265, TEST III 3

Problem 3 (12+6 points)

(a) Find an equation for the tangent plane to the graph of z=xy + cos(x−y) + 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).