Question

What is the limit as x approaches a of x-a/√x-√a

Answer 1

\[\frac{x-a}{\sqrt{x}-\sqrt{a}}=\frac{x-a}{\sqrt{x}-\sqrt{a}}.\frac{\sqrt{x}+\sqrt{a}}{\sqrt{x}+\sqrt{a}}\]

Answer 2

its quite simple ...

Answer 3

you can solve it by trick ..

Answer 4

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

Answer 5

\[\large \lim_{x\rightarrow a}\frac{x-a}{\sqrt{x} - \sqrt{a}}\]

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 \(\large 2\sqrt{a}\)

Answer 6

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

Answer 7

yes it will be \[2\sqrt{a}\]

Answer 8

I prefer @sirm3d method.

Answer 9

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