CYPRUS INTERNATIONAL UNIVERSITY MATH 102, Calculus II, 2021-2022 Spring Semester CIU FINAL EXAM Duration: 70 mins. Total 112 Ali Ozyapici-Grol-Gr05, Halil Gezer- Gr02-Gr03, Zalihe Yarkiner -Gr04 CYPRUS Student No: Name & Surname : Gr No : UNIVERSITY BOOKLET B Multiple Choice Questions. (7p each) 1. Given f (x, y) = yet . What is the ? (fly) a. ye' + xe b. ye" + xe" c. 2xey d. xy'ey +2yet e. xyet x+xy+x 2. lim (x.y) (0,0) =? x- xy a. co b. 0 c. 1 d. 2 e. Does Not Exist 3. The equation cos = r in polar coordinate can be represented in rectangular coordinate as a. x2 + y? =1 -bx2+y? = x*c. x2 + yz= y d. x2+y?=0 ex'ty = my 4. Consider the parametric equations x = 12 and y = a (t-1) . If the slope of the tangent line passing through at point (1,0) is 1, find a ? 1 b. 2 C. d. 0 e. 4 * x11. Consider the two dimensional function f (x, y) = Vx + y . Then evaluate ( f . ) ' + ( f, ) a. b. xty C. Vx 2 + y d. e. 1 12) Which of the following integral do we get if we interchange the order of integration ? a. fife f(x, y )dxdy b. fizz, f(x, y )dxdy c. fix fif(x, y )dxdy d. jamz So f(x, y )dxdy e. Size f( x, y )dxdy 13) The critical point (a, b) of the two dimensional function f (x, y) can be found as from system of two equations: 1 = f=(a,b)=0 and = f, (a,b) = 0. Which of the following point is the critical point of the given function ? f (x, y ) = 2xy- 5x2 - 2y2+ 4x -4 14)Which of the following vector is perpendicular to the given 2 vectors ? (Use dot product) u = and D = a. b. c. d. e. 15) Evaluate [' T ( + Amy )dy dx a. 10 b. 8 C. 6 d. 2 e. 4 b. = 16) If a = i + 2j + 3k and b = 31 + 2j + k, then find coso between the vectors a and b. C. = d.- e. =