## anonymous one year ago What is the limit as x approaches a of x-a/√x-√a

1. sirm3d

$\frac{x-a}{\sqrt{x}-\sqrt{a}}=\frac{x-a}{\sqrt{x}-\sqrt{a}}.\frac{\sqrt{x}+\sqrt{a}}{\sqrt{x}+\sqrt{a}}$

2. sohailiftikhar

its quite simple ...

3. sohailiftikhar

you can solve it by trick ..

4. sohailiftikhar

take derivative of above and below saperately then put the limit in answer ...

5. johnweldon1993

$\large \lim_{x\rightarrow a}\frac{x-a}{\sqrt{x} - \sqrt{a}}$ Becomes 0/0 so we can take the derivative of the top wrt 'a' and the the derivative of the bottom wrt 'a' $\large \frac{-1}{-\frac{1}{2}a^{-1/2}}$ $\large \frac{-1}{\frac{-1}{-2\sqrt{a}}}$ Which will come out to $$\large 2\sqrt{a}$$

6. johnweldon1993

*accidentally put a 2nd negative sign in the bottom fraction...only supposed to be one negative...answer remains the same however

7. sohailiftikhar

yes it will be $2\sqrt{a}$

8. Loser66

I prefer @sirm3d method.

9. sohailiftikhar

as you wish but if you have to solve extensive Q you should now the tricks also ...