A) 0
B) 1
C) 3
D) None of these
Correct Answer: B
Solution :
\[\underset{x\to 0}{\mathop{\lim }}\,\frac{\log (1+{{x}^{3}})}{{{\sin }^{3}}x}\]\[=\underset{x\to 0}{\mathop{\lim }}\,\frac{3{{x}^{2}}/(1+{{x}^{3}})}{3{{\sin }^{2}}x\cos x}\] [By using L- Hospital rule] \[=\underset{x\to 0}{\mathop{\lim }}\,\left[ \frac{1}{1+{{x}^{3}}}{{\left( \frac{x}{\sin x} \right)}^{2}}.\frac{1}{\cos x} \right]\]\[=\frac{1}{1+0}.{{(1)}^{2}}.\frac{1}{1}=1\].
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