Question

Please help with this limit! i don’t understand it.

Answer 1

Factorize the numerator as a difference of squares:

`x-s=(\sqrt x)^2-(\sqrt s)^2=(\sqrt x-\sqrt s)(\sqrt x+\sqrt s)`

Then

`\displaystyle\lim_(x\to s)(x-s)/(\sqrt x-\sqrt s)=\lim_(x\to s)(\sqrt x+\sqrt s)=\boxed{2\sqrt s}`