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## CALCULUS 2 FOR ENGINEERS

by: Dr. Filomena Hegmann

68

0

2

# CALCULUS 2 FOR ENGINEERS APPM 1360

Dr. Filomena Hegmann

GPA 3.76

Staff

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COURSE
PROF.
Staff
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Study Guide
PAGES
2
WORDS
KARMA
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## Popular in Applied Math

This 2 page Study Guide was uploaded by Dr. Filomena Hegmann on Thursday October 29, 2015. The Study Guide belongs to APPM 1360 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 68 views. For similar materials see /class/231877/appm-1360-university-of-colorado-at-boulder in Applied Math at University of Colorado at Boulder.

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Date Created: 10/29/15
APPM 1360 FINAL EXAM EQUATIONS Fall 2008 A shun iahle of iniegrals In ihe following a 0 12 71 u 1 ianh 1 u 0 ifu2 2 7 7 7 i i lt a 1 a2u27smh ltagt0 foragt0 W a a 5 7amp2 7u2 1 u 7coih 1 lt7 0 ifu2 gt o2 a a u 2 sin 1 lt7 0 for u2 lt o2 a 5 W 1 h 1 u 0 f o 7 7csc 7 or u uia2 u2 a 2 W h 1 u 0 f gt gt o 7 cos 7 or u a d 1 iu27a2 a 7 7 7sech 1lt3gt0 for0ltulta uio2 7o a a du 1 1 u du 1 1 u 2 2 47a2u2ian ltZgtC 87u u27a27gsec Z 0 foru gta Some circular and hyperbolic irig ideniiiies 1 cos2 c sin2 c 1 2 sin2 c 177591 5 cosh2 c 222 1 2 h 2 1 2 cos2 c W 4 cosh2 c 7 sinh2 c 1 5 sinh2 a In formulas 275 c remains xed as n 7 oo 1 a 1 lim 20 2 lim 11quot1 cgt0 5 lim 13 6 cltcc n7oo 7L naoo n7oo 7L 2 lim 1 4 lim equoto elt1 5 lim 710 elltcc n7oo n7oo n7oo 77 Here are some common Maclaurin Series and ihe values of c for which ihey converge 1 1xz2xquotE wquot l1llt1 ao 21 12 gtquot ltgtquot lllt1 1 75 1 7x c 11 gt ao E2 2 ez1x E ltoo 2 5 2n1 71V 2n1 c c c c 4 7 7 1quot7 7 5mm 7 3 J 5 2n 1 4 2n1 M lt ao 2 4 2n n 2 c c n c 71 c 5cosltwgt717 17lt71gtm7 W Mltoo 2 2 n a71 n 71 5ln1ec7 771quot 1 E 7 71lte51 n1 2 5 2n1 n 2n1 1 c e um 71 c 7i 7 1 7 lt1 an as w 35 lt gt2n1 Z 2H1 lxl ao 8 1Em1m1wxzm mm72 3777mm1mimn1 n7 ltfgtequot our 7 dy 2 7 ale 2 7 ale 2 dy 2 7 2 dr 2 2a E a d E 9 APPM 1360 A short table of integrals In the following a 7 039 du 71 u 139 12WSlnh ltEgt0 foragt0 2V sin 1 0 for u2 lt a2 xa iu du 71 u 339 X icosh ltEgt0 forugtagt0 du 1 u 4 77t 1 7 C 02u2 a an ltagt Some circular and hyperbolic trig identities 1V cos2zsin2m1 239 cos x 2 1 cos2m 2 3V sin2m Exam 1 Formula Sheet FALL 2008 1 itanhil lt3 0 ifu2 lt a2 I du 7 a 12722 7 1 icoth 1 0 ifuzgta2 a a du 1 1 u 639 WEcsch 2 0 foru70 du 1 1 u 739 mgsech 0 for0ltulta du 7 1 1 u 2 2 8V migsec E 0 foru gta 4V cosh2zsinh2m1 5 cosh2m cosh2z 1 V 2 6V Sinh2m cosh21 1 2

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