Evaluate : \(\displaystyle{\lim_{x \to 0}}\) \(x^3 cotx\over {1-cosx}\)

Solution :

\(\displaystyle{\lim_{x \to 0}}\) \(x^3 cosx\over {sinx(1-cosx)}\)

= \(\displaystyle{\lim_{x \to 0}}\) \(x^3 cosx(1 + cosx)\over {sinxsin^2x}\)

= \(\displaystyle{\lim_{x \to 0}}\) \({x^3\over sin^3x}.cosx(1 + cosx)\) = 2

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