10 Questions on Calculus II - Exam 2 | MATH 141, Exams of Calculus

Download 10 Questions on Calculus II - Exam 2 | MATH 141 and more Exams Calculus in PDF only on Docsity! MATH 141 SECOND EXAM OCT. 16, 1995 DR. ELLIS INSTRUCTIONS: 1. Answer each problem on a separate answer sheet. 2. Show all work. 1. Evaluate rn/2 22 r 5 [16] (a) sin x cos x dx [16] (b) x In x dx 0 2. Evaluate [12] (a) | ^^ dx [18] (b) x —— dx cos x I /2 ~•Vx - 4x + 5 [18] 3. Perform a partial fraction decomposition on the following rational function. Do not integrate. 2x2 - x + 1 2f 2 TT xx +1 [10] 4. (a) Use Simpsori' s Rule with 40 subintervals to approximate r 1 x e tan x dx. On your answer sheet write down what you -1 use for f(x), a, b, and n. Then write down the output of the calculator and the type of calculator you use. [10] (b) Use the inequality j^ ET * JL__ (b - a) 3 , where K = max |f"(x)| n ' to determine how many subintervals one would use to 2r / 2 approximate vl + x dx by means of the Trapezoidal Rule J 0 _o with error less than 10 ke1:10/95 a:141x2ell.f95