PS3 - MIT OpenCourseWare http://ocw.mit.edu 18.01 Single...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Fall 200 6 18.01 Problem Set 3 Due Friday 10/06/06, 1:55 pm Part I (10 points) Lecture 11. Fri. Sept. 29. Maximum-minimum problems. Read: 4.3, 4.4 Work: 2C-1, 2, 5, 11, 13. Lecture 12. Tue. Oct. 3 Related rate problems. Read: 4.5 Work: 2E-2, 3, 5, 7 Lecture 13. Thu. Oct. 5 Newtons method. Read: 4.6, (4.7 is optional) Lecture 14. Fri. Oct. 6 Mean-value theorem. Inequalities. Read: 2.6 to middle p. 77, Notes MVT Work: assigned on PS4 Part II (31 points + 8 extra credit) Directions: Attempt to solve each part of each problem yourself. If you collaborate, solutions must be written up independently. It is illegal to consult materials from previous semesters. With each problem is the day it can be done. 0. (not until due date; 3 pts) Write the names of all the people you consulted or with whom you collaborated and the resources you used, or say none or no consultation. (See full explanation on PS1). 1. (Friday, 6pts: 3 + 3) a) 4.3/28 (Use as variable the distance x from the foot of the ladder to the house. Check endpoints.) b) 4.4/28 2. (Tuesday, 2pts) Hypocycloid. Show that every tangent line to the curve x 2 / 3 + y 2 / 3 = 1 in first quadrant has the property that portion of the line in the first quadrant has length 1. (Use implicit differentiation; this is the same as problem 45 page 114 of text.) 3. (Tuesday, 7pts: 3 + 3 + 1) Sensitivity of measurement, revisited....
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PS3 - MIT OpenCourseWare http://ocw.mit.edu 18.01 Single...

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