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Question

Question: \[\lim_{x \rightarrow 0}\frac{x^{3}}{\sin x^{2}} =\]...

lim⁡x→0x3sin⁡x2=\lim_{x \rightarrow 0}\frac{x^{3}}{\sin x^{2}} =

A

0

B

13\frac{1}{3}

C

3

D

12\frac{1}{2}

Answer

0

Explanation

Solution

lim⁡x→0x3sin⁡x2=lim⁡x→0x2sin⁡x2.x\lim_{x \rightarrow 0}\frac{x^{3}}{\sin x^{2}} = \lim_{x \rightarrow 0}\frac{x^{2}}{\sin x^{2}}.x = (lim⁡x→0x2sin⁡x2)(lim⁡x→0x)\left( \lim_{x \rightarrow 0}\frac{x^{2}}{\sin x^{2}} \right)\left( \lim_{x \rightarrow 0}x \right)

= 1.0

= 0.