MCQ
$\mathop {\lim }\limits_{x \to 0} \frac{{\log [1 + {x^3}]}}{{{{\sin }^3}x}} = $
- A$0$
- ✓$1$
- C$3$
- Dએકપણ નહી.
$ = \mathop {\lim }\limits_{x \to 0} \frac{{3{x^2}/(1 + {x^3})}}{{3{{\sin }^2}x\cos x}}$
[By using $ L-$ Hospital rule]
$ = \mathop {\lim }\limits_{x \to 0} \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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