Evaluate The Following Limit. (3)

**TWiX** · February 16th 2010, 05:49 AM

Hello

evaluate:

$\lim_{x \to \frac{\pi}{4}} \,\ \frac{1-tan(x)}{sin(x)-cos(x)}$ .

without using l`hospital`s rule.

**General** · February 16th 2010, 05:53 AM

Originally Posted by TWiX

Hello

evaluate:

$\lim_{x \to \frac{\pi}{4}} \,\ \frac{1-tan(x)}{sin(x)-cos(x)}$ .

without using l`hospital`s rule.

$\frac{1-tan(x)}{sin(x)-cos(x)}=\frac{1-tan(x)}{sin(x)-cos(x)} \,\ \frac{cos(x)}{cos(x)}$

$=\frac{1}{cos(x)} \,\ \frac{cos(x)-sin(x)}{sin(x)-cos(x)}$

$=\frac{-1}{cos(x)} \rightarrow -\sqrt{2}$ as $x \rightarrow \frac{\pi}{4}$ .

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