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\[\LARGE \lim_{x \rightarrow a}\frac{x^\sqrt{2}-a^\sqrt{2}}{x-a}\]

I would consider rationalizing the numerator AND denominator first.

sqrt2 power of x and a

Never mind. Factor the numerator.

you there?

|dw:1355956723907:dw|

I am not looking for derivative of it, it is limit question..

\[ f'(x)=\frac{a^{\sqrt2}+\sqrt2 x^{\sqrt2-1} (x-a)-x^{\sqrt2}}{(a-x)^2}\]

...?

\[f(x)=x^{\sqrt2} ?\]

Yes, good.

I see now..

thanks..

but we cannot simplify it can we?

So that's where the a in coming from in the answer i guess :D

cool..

\[\large \lim_{h \rightarrow 0}\frac{(x+h)^2-x^2}{h}=2x ?\]