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Evaluate the following limit : \(\lim\limits_{\text x \to0}\cfrac{sin\,3\text x-sin\,\text x}{sin\,\text x}\)

lim(x→0) (sin 3x - sin x)/(sin x)

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Best answer

To find: \(\lim\limits_{\text x \to0}\cfrac{sin\,3\text x-sin\,\text x}{sin\,\text x}\)

We know,

Therefore,

{∵ cos 0 = 1}

= 2 × 1

= 2

Hence, the value of \(\lim\limits_{\text x \to0}\cfrac{sin\,3\text x-sin\,\text x}{sin\,\text x}\) = 2

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