# Problem 2-5: Evaluating Indeterminate Form

Calculate .

Solution

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1. chel says:

ahmm.. can you solved this one..
sqrt of x-2/x-4 as xapproaches to 4

1. Here you go:
$latex \displaystyle\lim_{x\to 4}\frac{\sqrt{x}-2}{x-4}=\displaystyle\lim_{x\to 4}\frac{\sqrt{x}-2}{x-4} \times \frac{\sqrt{x}+2}{\sqrt{x}+2}$
$latex =\displaystyle\lim_{x\to 4}\frac{\sqrt{x}^2-2^2}{(x-4)(\sqrt{x}+2)}=\displaystyle\lim_{x\to 4}\frac{x-4}{(x-4)(\sqrt{x}+2)}$
$latex =\displaystyle\lim_{x\to 4}\frac{1}{(\sqrt{x}+2)}=\frac{1}{(\sqrt{4}+2)}=\frac{1}{4}$