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Numerade Educator

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Problem 49 Hard Difficulty

Find the limit.
$ \displaystyle \lim_{x \to \pi/4} \frac {1 - \tan x}{\sin x - \cos x} $

Answer

$-\sqrt{2}$

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Video Transcript

he expressed the When you read here we have the limit as X approaches I for it of one minus 10 gin over a sine minus co sign this tangent becomes one minus sign over coastline and when we multiplied the top and bottom by co sign, we get the limits of X approaches. High four one minus sign. That's over. Co sign X over. Sign my guest co sign We want while I co sign, which gives us limit as X approaches by four co sign Linus Stein all over sine minus co sign terms Co sign This becomes equal to the limit as X approaches pi for negative sign Linus Co sign over sine minus co sign find co sign it cancels out to get limit as X approaches high Fours of one over co sign Negative. When we plug in pi forth, we get negative one over co sign of five bars. This becomes really to over two, which gives us an answer of negative route, too