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# Class Note for MATH 129 with Professor Glickenstein at UA

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COURSE
PROF.
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TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 19 views.

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Date Created: 02/06/15
76 8 We know that the ratio of the errors is 2 because LEFT20 has twice as many subdivisions as LEFT10 Hence if I represents the actual value of the integral 1 7 LEFT 10 2 I 7 LEFT 20 I 7 LEFT 10 7 21 7 LEFT 20 2 LEFT 20 7 LEFT 10 7 1 Thus the actual error for LEFT10 is I7LEFT 10 2 LEFT 20 7 LEFT 10 2 36517 7 38745 7004456 77 3amp3 I 1 7 fgquot equotdt 7 limb 7e 7 1 1 2 10 te tdt If we integrate by parts using u t dv equotdt so du dt v 75 we get 00 r27b11120 7ze Z0 tdt 7b 139 i bilge ab 1 F1 where we used L Hopital s rule to evaluate the limit b We wish to show 1 n1n1 n oo oo We ldt 7 n tn le tdt 0 0 So let s integrate 1 n 1 by parts using u t 11 equotdt so du ntn ldt and v 7equot 00 oo ine tdt lirn 7bne b ntnile tdt 0 b7oo 0 0n1 n c For the rst few positive integers we see that 1 1 1 1 2 1 1 21 1 2 1 4 32 1 5 432 and easily see that 1 n 7 1 40The de nition of energy on page 329 is b k E 11Q2dT a 72 where E is the energy required to separate two particles of charges ql and q2 actually these are the magnitudes or absolute values of the charges so they are always positive which are originally a distance a apart to a distance I apart k 9 109 is a constant we give this for E measured in joules qi measured in coulombs and distances 1 and I measured in meters To move two 1 coulomb charges from one meter to in nitely far apart we have E Layndr 1 r b k llm 7dr 7quot 9109j0ules

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