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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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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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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