limx-1+ (sqrt{x^{2}-x}/x-x^{2})

Question

limx->1+ (sqrt{x^{2}-x}/x-x^{2})

anonymous · Answer

$$\lim_{x \rightarrow 1} (\sqrt{x ^{2}-x} ) /x-x ^{2}$$

hartnn · Answer

is the question,
$\large \lim \limits_{x \rightarrow 1^+} \dfrac{(\sqrt{x ^{2}-x} )}{ x-x ^{2}} $

anonymous · Answer

@hartnn, I would think so, since most of the time homework problems give indeterminate form.

anonymous · Answer

@hartnn  yes it is.

hartnn · Answer

ok, then use $y= \sqrt y \times \sqrt y$
what about $(x-x^2)=...?$
anything cancels out ?

hartnn · Answer

or rather, factor out - *minus* first, 
-(x^2-x)

anonymous · Answer

i got 1/0.

hartnn · Answer

oh, you actually get, 
$\large \lim \limits_{x \rightarrow 1^+} \dfrac{1}{-(\sqrt{ x^2-x })}$
right ? 
now what about the denominator ? 
when x->1+, x is very very near to 1 but $\large x>1$
so, denominator will be positive or negative ?

anonymous · Answer

negative. so is it -infty ?

hartnn · Answer

YES, correct :)

anonymous · Answer

thank you :).  
i have one more question. can i mention you when i write ?

hartnn · Answer

yes, you can, and i saw that limit , tends to 3, right....

anonymous · Answer

yes. and i have one more which is i'm going to write now.

hartnn · Answer

ok, sure.