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a) Let f(x) = sin (2/x) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.)

a) Let f(x) = sin (2/x) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Let f(x) = sin (2/) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.) 2Vx +1 developed at c = b) The Taylor series for f(x) |x| < 1. Show the Taylor expansion for n = 1 and the remainder term. Given x = 0.01 and x = -0.01, how many correct digits do you get? 0 represents the function f for c) Convert the following from one base to another and write down your calculations as an expansion: (301)10 to (..)2 and (1.0111), to (..)8
Transcribed Image Text:a) Let f(x) = sin (2/) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.) 2Vx +1 developed at c = b) The Taylor series for f(x) |x| < 1. Show the Taylor expansion for n = 1 and the remainder term. Given x = 0.01 and x = -0.01, how many correct digits do you get? 0 represents the function f for c) Convert the following from one base to another and write down your calculations as an expansion: (301)10 to (..)2 and (1.0111), to (..)8
a) Let f(x) = sin (2/) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.) 2Vx +1 developed at c = b) The Taylor series for f(x) |x| < 1. Show the Taylor expansion for n = 1 and the remainder term. Given x = 0.01 and x = -0.01, how many correct digits do you get? 0 represents the function f for c) Convert the following from one base to another and write down your calculations as an expansion: (301)10 to (..)2 and (1.0111), to (..)8
Transcribed Image Text:a) Let f(x) = sin (2/) Compute the Taylor series for f developed at c= 0. (Hint: Compute it for sin (x) first, then use substitution.) 2Vx +1 developed at c = b) The Taylor series for f(x) |x| < 1. Show the Taylor expansion for n = 1 and the remainder term. Given x = 0.01 and x = -0.01, how many correct digits do you get? 0 represents the function f for c) Convert the following from one base to another and write down your calculations as an expansion: (301)10 to (..)2 and (1.0111), to (..)8
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