Taylor polynomial approximation (HELP ME)

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Homework Help Overview

The discussion revolves around determining the degree of a Taylor polynomial approximation for ln(1.2) centered at c = 1, with a focus on ensuring the error is less than 0.001. Participants are examining the expressions related to the remainder term in Taylor series and its implications for error estimation.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the derivation of a specific expression related to the error term and its components, particularly the role of the variable z. There is also a request for clarification on the steps leading to the inequality involving (n+1) and 5^(n+1).

Discussion Status

The discussion is active, with participants seeking clarification on the derivation of expressions and the rationale behind dropping certain terms. There is a mix of skepticism regarding the book's content and an exploration of the general process involved in Taylor polynomial approximations.

Contextual Notes

Some participants express confusion about the accuracy of the book's statements and the notation used, indicating potential discrepancies in the provided formulas. There is also an acknowledgment of missing parentheses in the original expressions, which may contribute to misunderstandings.

frasifrasi
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Ok, we are asked to determined the degree of the the taylor polynomial about c =1 that should be used to approximate ln (1.2) so the error is less than .001


the book goes through the steps and arrives at:

|Rn(1.2)| = (.02)^(n+1)/(z^(n+1)*(n+1)


but then, it states that

(.02)^(n+1)/(n+1) < .001

and there is an error pointing this expression to

1000 < (n+1)(5^(n+1))

--> I have no idea how the book arrived at this second expression, could anyone please explain?

- Also, if anyone knows, why was the z term left out in the second step?


Thank you.
 
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why was the z term dropped?

does anyone know?
 
I just don't believe your book has what you wrote. For one thing, |Rn(1.2)| = (.02)^(n+1)/(z^(n+1)*(n+1) is missing a ")". For another, the remainder formula has z in the numerator not the denominator- You can't make the error smaller by choosing z larger!
 
OK, in general how does this process work? I am having a little trouble following the steps...

*Yeah, I forgot the last parenthesis
 

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