Limit of Fraction: x→1 (sqrt(x)−x2)/(1−sqrt(x))

[nejnadusho]

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?

Thank you in advance.

 

[tiny-tim]

… just divide …

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

Hi nejnadusho!

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

 

[nejnadusho]

??

I am sorry I cannot do it.

I don't know how to do it

 

[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?

 

[nejnadusho]

Thank you nOW I got it.

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

 

[arunbg]

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

 

[nejnadusho]

Yes thanks