Taylor Series - Range of values

Click For Summary

Homework Help Overview

The original poster is tasked with finding the first four non-zero values for the Taylor expansion of exp(x) and determining the range of x values valid for this expansion. They express uncertainty about the latter part of the question.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the coefficients of the Taylor expansion and consider tests for convergence, such as the ratio test and integral test. There is questioning about how convergence relates to the validity of x values for the expansion.

Discussion Status

The discussion is exploring the relationship between the Taylor series and convergence. Some participants suggest that the series is valid where the sum converges, while others note that the series for exp is valid everywhere, indicating a divergence in interpretations.

Contextual Notes

There is a lack of explicit mention of convergence in the original question, leading to varied interpretations among participants regarding the conditions for the Taylor expansion's validity.

wombat4000
Messages
36
Reaction score
0

Homework Statement



im being asked for the first 4 non zero values for the taylor expansion of exp(x) which is simple, but then it asks for the range of x values that are valid for the expansion.

i have never come across ths before - any idea?
 
Physics news on Phys.org
From the first four coefficients of the taylor expansion you can guess what the nth coefficient is going to be. Is there then some test you can use to find out when a sum (don't worry about it being a taylor series!) converges?
 
ratio test? integral test?

but how will working out if the sum convereges help with obtaining the valid x values?
 
The ratio test is useful for calculating when taylor series converge. Each of the terms of your sum is in terms of 'x' so the ratio test tells you when the sum converges in terms of x.
 
the question doesn't mention sum or convergence?
 
The taylor series expansion is going to be valid where the sum converges, or alternatively you can just write that the taylor series expansion for exp is valid everywhere if you've been told this fact.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 11 ·
Replies
11
Views
3K
Replies
10
Views
2K
Replies
5
Views
2K
Replies
2
Views
3K
  • · Replies 13 ·
Replies
13
Views
10K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 10 ·
Replies
10
Views
4K