Evaluate : \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}

1.	Evaluate : \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}{x-\frac{\pi}{4}} \)
Answer» \(\lim\limits_{x \to π/4}\frac{sinx - cosx}{x - \frac{\pi}4}\) (0/0 type) \(=\lim\limits_{x \to \pi/4}\frac{cosx + sinx}1\) \(=cos\frac{\pi}4+sin\frac{\pi}4\) \(=\frac{1}{\sqrt2}+\frac1{\sqrt2}=\frac2{\sqrt2}\) = \(\sqrt2\)

Evaluate : \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}{x-\frac{\pi}{4}} \)

Answer»

\(\lim\limits_{x \to π/4}\frac{sinx - cosx}{x - \frac{\pi}4}\) (0/0 type)

\(=\lim\limits_{x \to \pi/4}\frac{cosx + sinx}1\)

\(=cos\frac{\pi}4+sin\frac{\pi}4\)

\(=\frac{1}{\sqrt2}+\frac1{\sqrt2}=\frac2{\sqrt2}\) = \(\sqrt2\)

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Evaluate : \( \lim _{x \rightarrow \frac{\pi}{4}} \frac{\sin x-\cos x}{x-\frac{\pi}{4}} \)

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