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Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sin(2+\text x)- sin (2 -\text x)}{\text x}\)

lim(x→0) (sin(2 + x) - sin(2 - x))/x

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Best answer

To find: \(\lim\limits_{\text x \to0}\cfrac{sin(2+\text x)- sin (2 -\text x)}{\text x}\)

We know,

Therefore,

Formula used:

= 2 cos 2 × 1

= 2 cos 2

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sin(2+\text x)- sin (2 -\text x)}{\text x}\) = 2 cos 2

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