General Instructions: This examination booklet contains six pages including the cover page, The exam has two parts. Part I contains ten short answer problems, Part II contains five workout problems. Part I [20 Marks] : Short Answer questions Write the most simplified answer on the space provided. 1. Evaluate the limit, lim an-100 2. Given the power series ) " i nyn35 Then the radius and interval of convergence respectively are and 3. Given that = = 2(5, y) implicitly and y' sin(2) = as +3zel, then : (-3,0, 1) - 4. The value of double integral Jf e-10(*+") dA, in_ 5. The area outside the circle with r = 2 and inside the circle r = Asino is 6. The minimum value of f(z, y/) = 2 + 13 on the line a + y = 4 is 7. Givent the series _ Then determine whether the series is (Absolutely convergent. Conditionally convergent, or Divergent). Ans. V25 - 1/ - 2 8. The value of the limit (20) 27 -1 - 4 9. The function f(x. y) = 3 ry(2 - ") if (x, ") / (0,0) is continuous at (0. 0) if (Er, 1/) = (0,0) (True/ False). 10. The equation of the tangent plane to the surface S given by the graph of 27 + 1/ = 3-2: at the point (2, 1, -3) is