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I’M ,/\0+ {00/ man am Hus all Him esp 9A b+a lnopenL CIP§ QOOd il/lCK OH ”ii/l8 MlCli’Ql’l/NATH“ Paper 1. After being kidnapped/on a trip to Canada, little Jimmy was able to see the speedometer of
the kidnapper’ s car, and carefully noted down the speeds every tenth of an hour (six minutes).
(Since they are in Canada,the speeds are in km/ hr). Jimmy was able to communicate these
speeds to his friend Juan Via text message, and Juan wants to ﬁgure out how far away Jimmy
is from Where they grabbed him. omework 4 timet 0.1f.2.3 .4 .5l.6 .7.8l.91
speedv(t) 306081l93 94 Using the midpoint rule, estimate the total distance (in km) that Jimmy was taken in the one 1
hour, that is, estimate the integral / 11(15) dt.
‘ 0 Under the assumption that —10 S v”(t) S 10, also determine the maximum error in your estimate.
ﬂ : AX 3‘ J—vo : i
n )0 = .1015 some} +£25.15 +8it+a5+55+16 +56%) M10
Mm: 60.5 WWI distance
Mayan/11L Error; KC”) my) _ ,IQ L aw MIG) WM 9‘10 K, 5V l Maximum error zgfo‘,
2. Approximate V/l ln(:c )cos(x x)dac usin Simpson’s rule with 4 intervals, aid give an estimate on the error of your approximation. You can get around the problem of 111(0) cos(0) not being deﬁned as follows. First integrate by parts,
sin(x) =1. ’ and then it is reasonable to take sin(0)/O— — 1 since limmmo So that you don’t kill yourself taking derivatives, 1‘ ll tell you that the 4th derivative of s1n(w) / :r is #9 h: L£ bebtwae: I1/5 aiid 1/:;)l:ji’ value Of ms Sni/ AX 3(‘P(X3+ 41olxa>+ ‘l'gﬂ'PLX. iléxh> 1.!
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 Fall '08
 Kerber

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