Lim of x->25 coming from the left (square root of x )- 5/(x-25)

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- Sep 19th 2010, 08:34 PMDeeEmEmFind the limit (if it exists) coming from the left?
Lim of x->25 coming from the left (square root of x )- 5/(x-25)

- Sep 19th 2010, 09:19 PMmr fantastic
- Sep 19th 2010, 10:36 PMCaptainBlack
- Sep 20th 2010, 03:48 AMHallsofIvy
Re brackets: (sqrt x)- 5/(x- 25) would normally be intepreted (by myself, anyway) as

$\displaystyle \sqrt{x}- \frac{5}{x- 25}$.

By the way, while mr. fantastic's "$\displaystyle t= \sqrt{x}$" substitution is probably simplest you could also think of $\displaystyle x- 25$ as a "difference of squares", $\displaystyle (\sqrt{x})^2- 5^2$ so the problem becomes

$\displaystyle \lim_{x\to 25}\frac{\sqrt{x- 5}}{(\sqrt{x+ 5})(\sqrt{x- 5})}$