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MAT286-2008Spring

# MAT286-2008Spring - Narne Firrr,l llxr,rrr\4ath 286 Sprirrg...

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Firr¿r,l llx¿r,rrr Narne \4ath 286 Sprirrg 2008 Cit'clc yor:r illstructr¡l's narnc: Sìr¿rw OliLrrpio lìolg C, Gr¿vcs S. Cra,r'cs Sbow youl work. You rnay uso :r, calculafor, but vou rnust writc-r the sk:ps yotL t¿lkc with tLre c¿ì,lculator. A col'l'¡rt ¿¡,nswcl with uo worì< will rìot rcccivc cr'ülit. Poirìt v¿rlucs are irulicateci by the proì.rlerri, 1, Suppose tliat thc slopc of 1;he Langcrrt lirro to a, furrctiou /(z) at :rrry r is givr:l ì.ry 'f 'þ:) - 4''z - 6z -1- 1' If the glaph 'U : .f (,r) gocä tlu'ough the poirt (1,2), firrd thr: fìrrrctiol /(:r). (J t) poirrts)

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2. Corrsidcr tlrc followiug filrtiorr ,l(er) ol the interval [0,2] : J (n) -- 6:t2 + sirr z t- 2, a) Use calculus to firrd the exact area bourcle<ì by the cluve ¿rxl tlrc r-axis on tlrc givelr irrterval. (Sh,out all str:7ts i,n,chuli,nq the apyn'op'itrte trttir\eri,ua,l,,iur:. ar¿rl tlrc a'uuluatior¡,s. No crr:di,t ui,l,l lse oí,uert .for pxtui,tlin¡¡ ortl11 lhe Jirta.l nttnterical ,ual,ue.) (10 poilts) b) Sct rrp, but do uot ev¿lnatc tlx; irrtcgrnl ther,t givcs the volulnc
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