# Limit of a fraction

1. Mar 21, 2008

Hi guys I have a question?

lim x->1 (sqrt(x)-x^2)/(1-sqrt(x))

What is the value of the limit of this function?

Is it possible to be (-2)?????

Or I AM WRONG?

2. Mar 21, 2008

### tiny-tim

… just divide …

The bottom of this fraction actually factors the top, so you can just divide it out, if you want …

3. Mar 21, 2008

???????

I am sorry I cannot do it.

I don't know how to do it

Last edited: Mar 21, 2008
4. Mar 22, 2008

### Gib Z

It might help to let $\sqrt{x} = u$ so that it becomes

$$\frac{u-u^4}{1-u} = \frac{ u(u^3-1)}{u-1}$$

Do you know how to factorize the u^3 -1 term?

5. Mar 22, 2008

Thank you nOW I got it.

No I don't know how to factorize this kind of terms

6. Mar 22, 2008

### arunbg

$$a^3-b^3 = (a-b)(a^2+ab+b^2)$$
Can you proceed?

7. Mar 24, 2008