Evaluate limx→0 sin(2+x)-sin(2-x)x - Mathematics

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Evaluate $lim_{x \to 0} \frac{\sin (2 + x) - \sin (2 - x)}{x}$

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उत्तर

We have $lim_{x \to 0} \frac{\sin (2 + x) - \sin (2 - x)}{x}$

= $lim_{x \to 0} \frac{2 \cos \frac{(2 + x + 2 - x)}{2} \sin \frac{(2 + x - 2 + x)}{2}}{x}$

= $lim_{x \to 0} \frac{2 \cos 2 \sin x}{x}$

= $2 \cos 2 lim_{x \to 0} \frac{\sin x}{x}$

= 2cos 2 as $lim_{x \to 0} \frac{\sin x}{x}$ = 1

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Limits of Trigonometric Functions

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पाठ 13: Limits and Derivatives - Solved Examples [पृष्ठ २२९]

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पाठ 13 Limits and Derivatives
Solved Examples | Q 5 | पृष्ठ २२९

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Limits of Trigonometric Functions

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Evaluate limx→0 sin(2+x)-sin(2-x)x - Mathematics

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Evaluate limx→0 sin(2+x)-sin(2-x)x - Mathematics

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