$\underset{x \to 0}{Lim} \frac{\sin [\cos x]}{1 + [\cos x]}$ ( [ . ] denotes the greatest integer function)

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Detailed Solution

As $x \to 0 \Rightarrow \cos x \to 1$
$∴ [\cos x] = 0 As x \to 0^{+} {or 0}^{-}, \cos x < 1 \Rightarrow [\cos x] = 0$
$\lim_{x \to 0} \frac{\sin [\cos x]}{1 + [\cos x]}$ = $\frac{0}{1 + 0} = 0$

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