Aspire Faculty ID #15256 · Topic: JAMIA MCA 2016 · Just now
JAMIA MCA 2016

$\displaystyle \lim_{x \to \frac{\pi}{4}} \frac{\sin x - \cos x}{x - \frac{\pi}{4}}$ is equal to …

Solution

his is the derivative of $\sin x-\cos x$ at $x=\frac{\pi}{4}$. $\,(\sin x-\cos x)'=\cos x+\sin x \Rightarrow \cos\frac{\pi}{4}+\sin\frac{\pi}{4} =\tfrac{\sqrt2}{2}+\tfrac{\sqrt2}{2}=\sqrt2.$
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