mathop {lim }limits_{x to 0} frac{{{x^3}}}{{s | vedclass

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(A) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{{x^3}}}{{\sin {x^2}}}$.We can rewrite the expression as: $\mathop {\lim }\limits_

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(A) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{{x^3}}}{{\sin {x^2}}}$.We can rewrite the expression as: $\mathop {\lim }\limits_{x 	o 0} \left( \frac{x^2}{\sin {x^2}} 	imes x ight)$.Using the property of limits $\mathop {\lim }\limits_{u 	o 0} \frac{u}{\sin u} = 1$,where $u = x^2$,as $x 	o 0$,$u 	o 0$.So,$\mathop {\lim }\limits_{x 	o 0} \frac{x^2}{\sin {x^2}} = 1$.Therefore,the limit becomes: $1 	imes \mathop {\lim }\limits_{x 	o 0} x = 1 	imes 0 = 0$.

$\mathop {\lim }\limits_{x \to 0} \frac{{{x^3}}}{{\sin {x^2}}} = $

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