# Pt find the degree 3 taylor polynomial t 3 x of func

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4.(1 pt) Find the degree 3 Taylor polynomialT3(x)of func-tionf(x) = (-5x+266)5/4R=.Correct Answers:16.(1 pt) The Taylor series forf(x) =x3at 2 isn=0cn(x-2)n.Find the first few coefficients.c0=c1=c2=c3=c4=Correct Answers:8126107.(1 pt) The functionf(x) =4xln(1+x)is represented as apower seriesf(x) =n=0cnxn.Find the FOLLOWING coefficients in the power series.c2=c3=c4=c5=c6=Find the radius of convergenceRof the series.8.(1 pt) Match the series with the right expression. (Use the
5.(1 pt) LetTk(x): be the Taylor polynomial of degree k ofthe functionf(x) =sin(x)ata=0.Suppose you approximatef(x)byTk(x), and if|x| ≤1, howmany terms do you need (that is, what is k) for you to have yourerror to be less than16? (Hint: use the alternating series approx-imation.)Maclaurin series.)1.n=03nn!2.n=0(-1)n32n(2n)!3.n=0(-1)n32n+12n+12
4.n=0(-1)n32n+1(2n+1)!A. arctan(3)B.e3C. cos(3)D. sin(3)Correct Answers:BCAD9.(1 pt) Match each of the Maclaurin series with right func-tion.1.n=0(-1)n2x2n+1(2n+1)!2.n=0(-1)n22nx2n(2n)!3.n=02nxnn!4.n=0(-1)n2x2n+12n+1A. 2sin(x)B. cos(2x)C. 2arctan(x)D.e2xCorrect Answers:ABDC
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Term
Fall
Professor
Roche
Tags
Math, Mathematical Series