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Consider the function S(x) = z+2 Determine the Taylor polynomial of degree n for f at 0. Show that for all r such that 0 < z < 1 lim Rof(x) = 0.

Consider the function S(x) = z+2 Determine the Taylor polynomial of degree n for f at 0. Show that for all r such that 0 < z < 1 lim Rof(x) = 0.

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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Transcribed Image Text:W Document1 - Microsoft Word (Product Activation Failed) File Home Insert Page Layout References Mailings Review View a ? A Find - A % Cut Calibri (Body) - 11 - A A =。三,年 外T Aal Aa AaBbCcDc AaBbCcDc AaBbC AaBbCc AaB AaBbCcL E Copy ae Replace IU - abe X, x* ab A I Normal I No Spaci. Heading 1 Change Paste A . Heading 2 Title Subtitle Format Painter Styles Select - Clipboard Font Paragraph Styles Editing 2·1·1· : 1:1·2•1• 3: 1· 4•I: 5. 1 6 L:7:L:8: L9.1 10. 1 11: I· 12: 1 13· L 14: I 15 : L 17. 1 18. I 9.1 · 10:I: 11 : 12: 13: 1 · 14: ' 15 : I' 17 I 18 Consider the function 2 S(x) = -, r+2 Determine the Taylor polynomial of degree n for f at 0. Show that for all r such that 0 <r < 1 lim Rn.of(x) = 0. n00 ull 02:07 PM 2021-10-08 Page: 1 of 1 E EI E E = 110% - + Words: 0
Expert Solution
Step 1

given function f(x)=2x+2

 

Theorem:

Suppose f(x)=Tn(x)+Rn(x) Then if,

 limn→∞ Rn(x)=0 for x-a<R then,

 f(x)=∑n=0∞f(n)(a)n!(x-a)n 

on x-a<R.

 

 

 

 

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