You are Here: Home >< Maths

# Alevel maths watch

1. How do I show that if x is small the expression root(1+x)/(1-x) is approximated by 1 +x +1/2xsquared
How do I show that if x is small the expression root(1+x)/(1-x) is approximated by 1 +x +1/2xsquared
By expanding the binomial up to the term in x^2.
3. What's a binomial
4. (Original post by M4cc4n4)
What's a binomial
A polynomial consisting of the sum of two terms.

in this case (1-x) and (1+x) are binomials, which can be approximately expanded when raised to a power using the binomial theorem, provided x is small.
5. But then I get 1+x+1/4xsquared and not 1/2x squares?
6. (Original post by NotNotBatman)
By expanding the binomial up to the term in x^2.
But then I get 1+x+1/4xsquared and not 1/2x squares?
7. (Original post by NotNotBatman)
A polynomial consisting of the sum of two terms.

in this case (1-x) and (1+x) are binomials, which can be approximately expanded when raised to a power using the binomial theorem, provided x is small.
Oh is that like C2 Binomial Expansion?
But then I get 1+x+1/4xsquared and not 1/2x squares?
What are you multiplying together?
9. (Original post by M4cc4n4)
Oh is that like C2 Binomial Expansion?
That's exactly what it is, yes.
10. (Original post by NotNotBatman)
What are you multiplying together?
I am multiplying( 1+1/2x)(1+1/2x)
11. As I have converted the root(1+x)/(1-x) to two binomials of (1+x) to the half and 1-x to the half and then expanded them each separately to get the first two terms of each and then multiplied these together
I am multiplying( 1+1/2x)(1+1/2x)
expand each binomial up to the term in x^2 and then multiply out and ignore terms of higher powers.
13. (Original post by NotNotBatman)
expand each binomial up to the term in x^2 and then multiply out and ignore terms of higher powers.
Thankyou so much!

### Related university courses

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: October 22, 2017
The home of Results and Clearing

### 2,601

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Keele University
Sun, 19 Aug '18
2. University of Melbourne
Sun, 19 Aug '18
3. Sheffield Hallam University
Tue, 21 Aug '18
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