13 Questions on Calculus 2 - Exam | MATH 211, Exams of Calculus

Download 13 Questions on Calculus 2 - Exam | MATH 211 and more Exams Calculus in PDF only on Docsity! Millersville University Name Department of Mathematics MATH 211, Calculus II, Final Examination May 6, 2008, 8:00AM-10:00AM Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. (8 points) Use integration by parts to compute the following indefinite integral. ∫ (2x2 − 9)e2x dx 2. (8 points) Use a partial fractions decomposition to compute the following indefinite integral. Simplify your answer. ∫ x2 − 4 x3 − 2x2 − 15x dx 6. (8 points) Find a power series in x representation for the function f(x) = 2 1 + 4x2 . State the radius of convergence for the power series. 7. (6 points) Consider the curve described by the parametric equations x = t3 − 3t y = t2 + 2t Find the slope of the tangent line to the graph of the parametric curve when t = 1. 8. (8 points) Identify the type of conic section represented by the equation below. Find all the foci, vertices, asymptotes, and the directrix if appropriate. x2 9 − (y − 2)2 4 = 1 9. (8 points) A water tower is spherical in shape with a radius of 50 feet, extending from 200 feet to 300 feet above ground. Compute the work done in filling the bottom half of the tank with water from the ground level. You may use the fact that water weighs 62.4 lbs/ft3.