# Polynomial Infinity Limit

1. Jan 27, 2010

### mohamedibr752

Hi, I'm in Engineering Foundation.
I'm stuck in one limit question.

Find the limit :_
**********________
Lim (3x + V 9x^2 - x )
x-> -infinity

by substitution it gives ( inf - inf )
I tried to solve it and get -inf

Can anyone help me please ?

2. Jan 27, 2010

### tiny-tim

Welcome to PF!

Hi mohamedibr752! Welcome to PF!

(have a square-root: √ and an infinity: ∞ )
(no need to shout! )

Hint: it's the same as limx->-∞ 3x + 3|x|√(1 - 1/9x))

Last edited: Jan 27, 2010
3. Jan 27, 2010

### mohamedibr752

Thank you for your help .. I get it now ..
but why did you write it 3x(1 + ...
I think it is 3x(1 - ...
because the x is approaching -∞ so as to remove absolute 3x we have to put - to make sure that the 3x is positive ??

The answer I get is -∞.

Thank you

4. Jan 27, 2010

### tiny-tim

Hi mohamedibr752!
I goofed!

I did correct it before you answered, but I think you missed the change.
No, try again … expand the square-root and do a bit of cancelling.

5. Jan 27, 2010

### Mentallic

Wait, what? No the answer isn't $-\infty$.

Look again at $$3x+3|x|\sqrt{1-\frac{1}{9x}}$$ as the limit approaches $-\infty$. It is definitely not what you stated.

6. Jan 27, 2010

### evagelos

Multiply by $$\frac{3x -\sqrt{9x^2-x}}{3x-\sqrt{9x^2-x}}$$ ....... and then divide by x,

then take the limit