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

# Limits Help watch

1. What is the limit of f(x) as x approaches infinity, where f(x) = [((x^2)+3x)^0.5) - x]

That should read; open bracket, x squared plus 3x, close bracket to the power of half, - x.

I've tried to use a binomial expansion, firstly I took out a factor of (3x)^0.5

Which yielded; (3x)^0.5 [1+(x/3)]^0.5 - x

I had used the binominal expansion 1+nx+n(n-1)x^2/2!+.... where n<1 however I cannot manage to obtain the correct answer of 3/2.

Help would be appreciated
2. Try rewriting f(x) by rationalising it
3. (Original post by Dalilsp)
Try rewriting f(x) by rationalising it
Ok, I just tried that now...

3x/[(x^2+3x)^0.5+x]

Numerator: 3
Denominator: Sqrt(3/x)[expansion terms] + 1

As x--->infinity.

Denominator tends to 1? Yielding a limit of 3?

Wrong though, I've made a mistake somewhere
4. (Original post by ArcRaman)
Ok, I just tried that now...

3x/[(x^2+3x)^0.5+x]

Numerator: 3
Denominator: Sqrt(3/x)[expansion terms] + 1

As x--->infinity.

Denominator tends to 1? Yielding a limit of 3?

Wrong though, I've made a mistake somewhere

in the denominator

x factor will be cancelled

and as x-> infty the denominator

5. (Original post by ztibor)
in the denominator

x factor will be cancelled

and as x-> infty the denominator

Thanks man

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: September 24, 2014
Today on TSR

### Four things top students are doing

Over the Easter break

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