222-robbin-07spex02-pt2

222-robbin-07spex02-pt2 - Name _________ __ I 133319 in:...

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Unformatted text preview: Name _________ __ I 133319 in: Math 222, Exam II Continued, Monday, March 9, 2007 Circle your section: 323 324 326 327 328 329 330 331 113 INGRAHAM B3129 VAN VLECK B135 VAN VLECK 119 VAN VLECK B337 VAN VLECK B305 VAN VLECK B329 VAN VLECK B333 VAN VLECK SHOW YOUR REASONING. 30 Points v TR 08:50—09:40 TR 09:55—10:45 TR 11:00—11:50 TR 11:00—11:50 TR 12:05—12:55 TR 13:20—14:10 TR 14:25~15:15 TR 15:30—16:20 l 30 Points - 30 Points Total POints Georgiou, Nicos Georgiou, Nicos‘ Ache, Antonio Beros, Achilles Ache, Antonio Beros, Constantinos Beros, Constantinos ' Beros, Achilles I. (30 points.) (i) Find a polynomial P of degree 4 such that 13(0) = 1, P’(0) = 3, P”(0) = 5, P<3>(0) = 7, P‘(4)(0) = 9. (ii) Find a polynomial ‘P of degree 4 such that P(6) = 1, P’(6) = 3, P”(6) = 5, P<3)(6) = 7, 1390(6) = 9. (You need not simplify your answer.) II. (30 points.) (1) Find the first 5 coeflicientsco, . . . ,04 in the Taylor series I 00 e (1_$2) =chx' n=0 Hint: Be smart. (ii) Suppose that f(:1:) = 1.+ ac — 3:4 + 0(334) and 9(33) 2 2 + $3 + 0(934). Find the (there is only. one) polynomial P(a:) of degree 4 such that f (3:)g(cc) = P(ac) + 0(234). III. (30 points.) (i) Calculate (8.5)1/3 approximately using the the second order Taylor poly— nomial for the function f (ac) = (8 + 201/3. (ii) Estimate the error |(8.5)1/3 — P2(0.5)| between (8.5)”3 and the answer you got to part (ii). ‘ IV. (30 points.) (i) Find real numbers a" and 6 such that ' 1 + 22' =: rem. (ii) Find real numbers 7" and (9 such that —1 + 22' = re”. V. (30 points.) Find real numbers A and gb so that A cos(t — 4)) = 12 cos(t — + 12 cos(t —— ém’). ...
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222-robbin-07spex02-pt2 - Name _________ __ I 133319 in:...

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