MATH 201 Exam 1, Fall 2012

Fall 2012-2013 Quiz 2 Date: November 23 Prof, M. Egeileh Math 201 - Sections 24 to 26 Duration: 1 hour Problem 1 (answer on page 1 of the booklet) Find the domain and ran ge of the function f(z, y, z)= f/P+Pre en region i ?— 9. Determine if the . Also, determine if the domain is page 2 of the booklet) local minima, and saddle points of the function 2° + 6x? — 4y8 + 3y?. (16 pts) f(x,y) = Problem 3 (answer on page 3 of the booklet) Find the tangent plane and the normal line to the surface z = oa 3 rae at the point (1,2, 1). (16 pts) Problem 4 (answer on page 4 of the booklet) For each of the followin g limits, say if it exists or no, justifying your answer. (7 pts each) zis +c b)) tn (Ee Die B (z,y)+(0,0) 23 + y? sin x zy? c) lim (z,v)+(0,0) r+y (=¥)+(0,0) 2? — 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 = 67 — 93 V#(3,2,5) =F 2748, 94(3,1,3) <7 47, 9 f(@,1,3)=5, F@ as) =e em i Let aerate ite 7 Se en and w= f(z,y,2z). = oe 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) € normal to the surface f(z, y, z) = 3. (7 pts) t to the curve w(r,s) = 2(2r + s) in the rs-plane. (8 pts)