HW12 - Calculus 1A: Homework Assignments. Notes and Hints....

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Unformatted text preview: Calculus 1A: Homework Assignments. Notes and Hints. Revised 1/19/09 Spring 2009, TT 3:30pm - 5:00pm, Room 105 Stanley Hall Instructor: Professor Zvezdelina Stankova HW12. Read 5.1-5.2, Appendix E. Solve and Write Problems: (1) App. E: #6,10,16,22,30,36. (a) #16: the last term gives away a lot! Your dummy variable basically replaces the variable n . (b) #22-30: first expand the sum (i.e., write it out without the notation); after that in #30: use the formula for the sum of the first several natural numbers; if in doubt whether you got the right answer: check by hand for several small values of n . (2) 5.1: #2,4,18,20,22,26*. (a) #18: choose one of R n , L n or M n approximations, partition the interval into n pieces, find the right endpoints (respectively, left endpoints or midpoints), and write R n ( L n or M n ) as a sum. Finally, in front of what you get, put a limit with n approaching infinity (to fit with the definition of area), and you are done. Compare with #17: there they have gone one step further by writing the sumand you are done....
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