MATH 201 Exam 2, Spring 2019

Math 201—Exam 2 (Spring 19) Profs. F. Abi-Khuzam, B. Shayya, and T. Tlas e Please write your section number on your booklet. e Please place your student ID card on the desk in front of you. e Please answer each problem on the indicated page(s) of the booklet. Any part of your answer not written on the indicated page(s) will not be graded. e Unjustified answers will receive little or no credit. Problem 1 (answer on pages 1 and 2 of the booklet.) Consider the function f(x,y) = 8/(4 — 2? — y?). (i) (10 pts) Find Domain f and Range f. Decide if Domain f is an open region, a closed region, or neither. Also decide if Domain f is bounded or unbounded. Hs (ii) (10 pts) Find the tangent line of the level curve f(x, y) = [Sat the point (3, 4). = &| Problem 2 (answer on pages 3 and 4 of the booklet.) a (a) (8 pts) Does y' lim (zy)>(0.0) 8 + y4 exist? Why or why not? (b) (8 pts) Does lim. ay (zu)(0,0) 8a + 4y exist? Why or why not? Problem 3 (answer on pages 5 and 6 of the booklet.) (16 pts) Find the tangent plane and normal line of the (3,—-1,9). am Problem 4 (answer on pages 7 Consider the function f(z,y) = (i) (8 pts) Find all loca. (ii) (8 pts) Find