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Math  /  Calculus

QuestionFind lim⁡x→π4g(x)\lim _{x \rightarrow \frac{\pi}{4}} g(x) for g(x)=cos⁡x−sin⁡x1−2sin⁡2xg(x)=\frac{\cos x-\sin x}{1-2 \sin ^{2} x}. Options: (A) 0 (B) 12\frac{1}{\sqrt{2}} (C) 2\sqrt{2} (D) Limit does not exist.

Studdy Solution
implify the limit.
lim⁡x→π4−2−2=2\lim{x \rightarrow \frac{\pi}{4}} \frac{-\sqrt{2}}{-2} = \sqrt{2}So, the limit of g(x)g(x) as xx approaches π4\frac{\pi}{4} is 2\sqrt{2}.

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