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Math Help - Evaluate The Following Limit. (3)

  1. #1
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    Evaluate The Following Limit. (3)

    Hello

    evaluate:

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

    without using l`hospital`s rule.
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  2. #2
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    Quote Originally Posted by TWiX View Post
    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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