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sample exam solutions

sample exam solutions - UNIVERSITY OF WATERLOO FINAL...

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UNIVERSITY OF WATERLOO FINAL EXAMINATION Term: Fall Yea.J:~tJU~ Student Name UW Student ill Number Course Abbreviation and Number MATH 117 Course Title Calculus 1 for Electrical & Computer Eng. Sections(s) 001,002, 003, 004, and 005 Sections Combined Course(s) SYDE III Section Numbers of Combined Course(s) 001 Instructor(s) o B. Ingalls o D. Harmsworth (BE) o G. Tenti o D. Harmsworth (CE) OM Scott OD,E. Chang Date of Examination December 12,2005 Time Period Start time 12:30 p.m .. End time: 3:00 p.m. Duration of Exam 2.5 hours Number of Exam Pages (including this cover sheet) 11 Exam Type S pedal Materials Additional Materials Allowed Formula Sheet. Marking Scheme: Question 1 2 3 4 5 6 7 Totals Marks 15 15 15 15 15 15 10 100 Score }
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Fal12005 MAre 117/SYDE 111- Final Examination 1. Evaluate the following integrals: __ i_:: ~ t ~ 4- c.. :1"(1--\) A- -,.: :x.--\ =") ,-= A:dx-I) ~ % (j.-\) + Cx,;I.. \=.-~ 51> (S:::-\ ~~~inj x.:; 0 I \ -: CIS" G:;. \ Se\\~~ :L~ \ O~ A+e. ) A; -\. Sb \~(. -2 -\e.~~ - 1\ } ).. (c) s: 11 sin(x)dt J).v..-\-k.:, ~ .. ::: ) ~II;:; S~l\ ,., lb .. 5~ ~v- '= .~h.l,,- v; - (.0, iC. J "'Gla. ""I \k{;).. t. ~ ~/a- ~ .... J X SI" :t. cl.;:J., :: - X (..0> X- \ + J ~~c.o.s:x.. c\;t... ~ ~ 0 :::: "V.h o -\- J.. j ~ (0.5 ~ 11. . \low v...~ u.:; ::t J J. v,; (.oS. x.l o ~ J..\)..~ lb .. ) Y ~ si" -;.. . Page 2 ofll
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MATH 117/SYDE 111 - Final Examination Fall 2005 2. (a) Show that f j(x)dr = if(x) - f if'(x)dr, and use it to evalueate f sin-I (r)dr . Le\ v..~+h.), cl'J-=J..~) (~) St> !v-.:: rl:;(.)~:1) -J=.J.. J\ (~) h.:: ) I,).~'J := ~'J - )"c\.",:: x. t 1,,-' - j A r(:x.)!}..) 0.'> ret~(~. ~o',.J\ ,\- ~ b.);: 51,,':t / ~he" r 1.;(,) = t\ ~;:.
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