Recitation Problems: L'hopital's Rule and Optimization, Assignments of Mathematics

Download Recitation Problems: L'hopital's Rule and Optimization and more Assignments Mathematics in PDF only on Docsity! Recitations 28, 29 MA113:004{006 1, 3 December 1998 Fall 1998 Below is a selection of problems related to section 4.5, L'hopital's rule and 4.6, optimization problems. These problems will not be collected or graded. However, you should understand how to work each of these problems. You should begin working on these problems in groups in recitation. You will probably want to nish these problems outside of class. If you have questions, please ask your TA or instructor. If you nd a problem dicult, consider working similar problems from the text for additional practice. Announcements: 1. The nal for this course is in CB122 (note room change!) from 8:30{10:30 on Monday, 14 December 1998. 2. The last project is due on 4 December 1998. 1. Written homework due at 10am on 7 December 1998. x4.5 14, 48. x4.6 10, 30. 2. Section 4.5 #1, 3, 5, 7, 9, 13, 15, 43, 47. 3. Section 4.6 #1, 3, 9, 11, 17, 21, 31. 4. Find two functions f and g where lim x!0 f(x) g(x) = 7 and lim x!0 f 0(x) g0(x) = 3: Can you replace 3 and 7 by any numbers a and b? 5. (Review) Di erentiate e3x 2 and p 1 sin2 x. 6. (Review) Suppose that the two shortest sides of a right triangle a(t) and b(t) vary with time and after t seconds a(t) = t2 meters and b(t) = t meters. (a) Let c(t) be the hypotenuse and nd c0(t). (b) Let be the angle opposite the side whose length is b(t) and nd 0(2). (c) Why is 0(t) = 0(t)? Here, denotes the angle opposite the side whose length is a(t). November 25, 1998