quiz3 - ~ \ 00 ",0</= ~x~Y2-L C~)XZq1 (}'l :::: C...

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/ I ..l. ., - - -- Name 15 Math 253 Quiz 3 (20 points) 1. (5 points) Evaluate the indefinite integral as an infinite series: f xcos(x2)dx oC! 47>71 00 L ( ) 'h X Z . QI.trn. .1 -( ) '" L. (-,) £. ~',. X CM (x )~ '.271) I (/)-;;;0 12. .?" ) I iO1 ;-~ ~.. L"'" {, 2... 0<:) AI X...,7H r K ~(x1.)cJX::: L. (- f) + L J !/1 :::u CZtf}'1.f- 2. )(g ?) ) ! 00 fJ1 X Zfw.J. L C+ L (-t) - Answer ,1)1~Q (t.r??f- 2)( lIt) I ~ 2. (5 points) Find the sum of the series: 1-1n2+ (ln2)2 - (ln2)3 2! 3! +... 00 tr) ::: l (-/)~ i) rn ~ 01' - (/ OC7) -;: l t:~ L) -0n2- I -= e "" -"I rn 'I' '- (.; ... f}J~ () Answer - en L 1 ( Il e = e~i1i :=c~
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__I 3. a)(5 points) Use the binomial series to find the Maclaurin series of: f(x) = fl+;2
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Unformatted text preview: ~ \ 00 ",0</= ~x~Y2-L C~)XZq1 (}'l :::: C C.fi)~ i'z C~-I)C~'-Z).' Ci,-It. ..,) Cl)(-~)[- '<;)(-~;~ , ~-~" 'IA f-~II/t. '-;:::-(-t) I"?>,-' (LU-~ ZYJ ffI , H Answer 00 ?1 iCX);;o L H 1'3'-(Z4.~ 211) ;1\;:0 L) 2 ')'1 rn 1-X .. b)(5 points) Use part a) to evaluate f(1O)(O). [ _ ~ (\.t)/ . ) ' oi fO (-tj' 1,3, ~. 7 " to-..p) X-':t' .~ c..~~-\ .---:--,5' 1 \ 0 ~ 1\.;:c6 I\~a:) :.l. G . Answer f_l\ ~) "\ (0 ') ::: ..-1o~ . (-ly>.1.8'5-7.1 . 25.5 j .....
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This note was uploaded on 08/17/2009 for the course MATH 253 taught by Professor Poplicher during the Spring '08 term at University of Cincinnati.

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quiz3 - ~ \ 00 ",0</= ~x~Y2-L C~)XZq1 (}'l :::: C...

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