Math 1312 Final Exam Prep: Info, Study Tips, & Practice - Prof. Donna I. Wilson, Exams of Calculus

Download Math 1312 Final Exam Prep: Info, Study Tips, & Practice - Prof. Donna I. Wilson and more Exams Calculus in PDF only on Docsity! Math 1312 Name D.Wilson Final Exam Information • The final exam will be given on Tuesday, May 6, 1 - 4PM. There are no make-ups. • A graphing calculator may not be used during the first 45 minutes of the exam. Some study suggestions: • Redo the exams and quizzes. The solutions are on WebCT. • There is an extra credit quiz on WebAssign. Office Hours and Review: • On Friday, May 2, 10AM - 12PM, Bell 130A, we can go over problems from this worksheet. • I’ll be available for office hours on Monday, May 5, 12 - 2PM, in Bell 216. More Practice Exercises 1. Determine whether these series converge or diverge. Show all work. (a) ∑ n ln n (b) ∑ ln n n4 (c) ∑ 2n n3 (d) ∑ n en 2. Find the exact sum of the series: (a) ∞∑ n=−2 ( 5 7 )n (b) ∞∑ n=1 1 9n2 + 15n + 4 3. Below are the Taylor series about x = 0 for some functions. • ex = ∞∑ n=0 xn n! • sin x = ∞∑ n=0 (−1)n x2n+1 (2n + 1)! • cos x = ∞∑ n=0 (−1)n x2n (2n)! • 1 1− x = ∞∑ n=0 xn Use these series to write the first four nonzero terms of the Taylor series about x = 0 of these functions: (a) f(x) = sin(3x4) (b) f(x) = x cos(2x3) (c) f(x) = ln(1− x2) (d) f(x) = x3e−5x 4. Integrate the following. (a) ∫ ex arctan(ex) dx (b) ∫ dx x2 √ x2 + 1 (c) ∫ √ x2 − 9 x dx (d) ∫ (sin θ + cos θ)2dθ (e) ∫ dx (4− x2)3/2 (f) ∫ cos( √ x)dx