# Limit of a fraction

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?

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tiny-tim
Homework Helper
… just divide …

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

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

???????

I am sorry I cannot do it.

I don't know how to do it

Last edited:
Gib Z
Homework Helper
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?

Thank you nOW I got it.

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

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

Yes thanks