x Turn on thread page Beta
 You are Here: Home >< Maths

# what values a taylor expansion is valid for watch

1. Hi, im really confused as to how to work out what values a taylor expansion is valid for. could someone please give me some help.

heres an example.

this is a maclaurin expansion (a=0) for
f(x)=ln(1+2x)

expansion up to is

2x-2

the answer says expansion is valid for mod 2x <1 so mod x<1/2

i dont understand why this is.
thank you
2. The expansion involves higher and higher powers of x. For 2x<1, the higher powers will be fractional and so will decrease in magnitude (e.g. 0.5^2 = 0.25) For 2x>1 this is not the case: higher order temrs will be larger than 1, meaning the series will diverge to infinity.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 15, 2010
Today on TSR

### Been caught plagiarising...

...for the 2nd time this year

### Mum says she'll curse me if I don't go to uni

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE