MATH 201 Exam 1, Spring 2013

CC EESS'S Se Fall 2012-2013 Quiz 2 Prof. M. Egeileh Date: November 23 Math 201 - Sections 24 to 26 Duration: 1 hour ge of the function f(z,y,z) = /2?¢ y’ + z?—9. Determine if the domain of f is an open regi i i - Also, determine if the domain is Problem 2 (answer on page 2 of the booklet) Find all local maxima, local minima, and saddle points of the function F(z, y) = 225 + 62? — 4y3 + 342. (16 pts) Problem 3 (answer on page 3 of the booklet) Find the tangent plane and the normal line to the surface z = oe 3 mae at the point (1,2, 1). (16 pts) Problem 4 (answer on page 4 of the booklet) For each of the following limits, say if it exists or no, justifying 2 — pane Yee (e* — 1)(e 1) (z,¥)> (0,0) =+ y your answer. (7 pts each) a tee (=¥)>(0,0) z? — 27 —y Problem 5 (answer on pages 5 and 6 of the booklet) Suppose that f(z, y, z) is a differentiable function of three variables which, at the point (3, 2,5), decreases most rapidly in the direction of A = 6; — 93 = wea, So wee 5 = VI8,2,5)=7T- 54k, 973,18) =74 7 9p 2,1,) f(3,1,3)=5, 7(8,2,5)=3, £(8,2,5) = 11. Let r=r+s, Van 3) 2 Oe er and w= f(z,y, 2). 1. Find = and aad at the point (r,s) = (2, 1). Then estimate w(2.3, 1.4). (15 pts) 1 What are the directions of zero change in w at the point @s= G, >) ? (7 pts) ormal to the surface f(z, y, z) = 3. (7 pts) gent to the curve w(r, s) = 2(2r +s) in the rs-plane. (8 pts)