# Find the limit (if it exists) coming from the left?

• Sep 19th 2010, 08:34 PM
DeeEmEm
Find 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 PM
mr fantastic
Quote:

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

Substitute $t = \sqrt{x}$: $\displaystyle \frac{\sqrt{x} - 5}{x - 25} = \frac{t - 5}{t^2 - 25}$. Your job is to calculate the limit of this as t approaches 5.
• Sep 19th 2010, 10:36 PM
CaptainBlack
Quote:

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

If I were you I would seriously reconsider my use of brackets here.

MrF has made a guess at what is meant, but you really really don't want to have to rely on his/our psychic abilities.

CB
• Sep 20th 2010, 03:48 AM
HallsofIvy
Re brackets: (sqrt x)- 5/(x- 25) would normally be intepreted (by myself, anyway) as
$\sqrt{x}- \frac{5}{x- 25}$.

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