# MAT-232-WA10.docx - Thomas Edison State College Calculus II...

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Thomas Edison State College Calculus II (MAT-232) Section no.: Semester and year: OCTOBER 2017 Written Assignment 10 Answer all assigned exercises, and show all work. Each exercise is worth 10 points. Section 8.7 6.Find the Maclaurin series (i.e., Taylor series aboutc= 0) and its interval of convergence.
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10.Find the Taylor series about the indicated center, and determine the interval of convergence.
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f' (x)=−sinx ,f(π2)=−sin(π 2 ) =1 f' ' (x) =−cosx ,f(π2)=−cos(π 2 ) =0 f' ' '(x) =sinx ,f(π2)=sin(π 2 ) =−1 f4 (x)=cosx, f(π2)=cos(π 2 ) =0 11!(x+π2)13!(x+π2)3+15!(x+π2)517!(x+ π 2)7k=0 1k(2k1)! (x+ π 2 ) (2k1) limk →∞|1(k+1 ) (x+ π 2 ) 2(k+1)1 (2(k+1)1)!(2k1)! 1k (x+ π 2 ) 2k1| =limk →∞ |1 2k(2k+1) | =0 converges for all x intervalof convergenceis(∞ ,∞)

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