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

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

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

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

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

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

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

5 views Answered 2023-02-05 15:29

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