8 Questions on Old Exam 5 for Calculus I | MATH 141, Exams of Mathematics

Download 8 Questions on Old Exam 5 for Calculus I | MATH 141 and more Exams Mathematics in PDF only on Docsity! Exam 5, Math 141, 1996 PRINT Your Name: Section: There are 8 problems on 4 pages. Problem 4 is worth 30 points. Each of the other problems is worth 10 points. SHOW your work. CIRCLE your answer. NO CALCULATORS! 1. State both parts of the Fundamental Theorem of Calculus. 2. Let A(x) = x∫ 1 1 t dt . Find A′(x) . 3. Compute π/2∫ 0 sin4 x cos x dx . 4. (10 points for each part) Consider the region R which is bounded by y = x2 , x = 2 , x = 3 , and y = 0 . (a) Find the area of R . (b) Find the volume of the solid which is obtained by revolving R about the x− axis. (c) Find the volume of the solid which is obtained by revolving R about the y− axis. 5. Let f(x) = −x3 + 3x2 . Where is f(x) increasing, decreasing, concave up, and concave down? What are the local extreme points and points of inflection of y = f(x) . Graph y = f(x) . 6. Find the length of y = 2x3/2 between x = 1/3 and x = 7 . 7. Find the points on the curve y2 + 2x = 9 which are closest to the point (0, 0) . 8. Find the area of the surface which is generated by revolving y = x3/3 , for 1 ≤ x ≤ √7 , about the x− axis.