Calculating Limit: Need Help Evaluating √x-√a/(x-a)

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Homework Statement



Evaluate the limit

Lim (√x-√a)/(x-a)
x→a



I am not sure how to solve this. I asked my classmates and they do not know either. Help would be much appreciated!
 
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Looks like you have type zero-over-zero, thus permitting use of L'Hospital's rule, which says you can take the derivative of the top and the derivative of the bottom and then evaluate the limit.
 
TyChi said:

Homework Statement



Evaluate the limit

Lim (√x-√a)/(x-a)
x→a

I am not sure how to solve this. I asked my classmates and they do not know either. Help would be much appreciated!
You might consider rationalizing numerator. Then there's no need to use L'Hôpital's rule.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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