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

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(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{x 	o 0} \frac{{{x^3}}}{{\sin {x^2}}}$.આપણે પદાવલિને આ રીતે લખી શકીએ: $\mathop {\lim }\limits_{x 	o 0} \left(

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(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{x 	o 0} \frac{{{x^3}}}{{\sin {x^2}}}$.આપણે પદાવલિને આ રીતે લખી શકીએ: $\mathop {\lim }\limits_{x 	o 0} \left( \frac{x^2}{\sin {x^2}} 	imes x ight)$.લક્ષના ગુણધર્મ $\mathop {\lim }\limits_{u 	o 0} \frac{u}{\sin u} = 1$ નો ઉપયોગ કરતા,જ્યાં $u = x^2$,જેમ $x 	o 0$,તેમ $u 	o 0$.તેથી,$\mathop {\lim }\limits_{x 	o 0} \frac{x^2}{\sin {x^2}} = 1$.આમ,લક્ષનું મૂલ્ય: $1 	imes \mathop {\lim }\limits_{x 	o 0} x = 1 	imes 0 = 0$ થાય છે.

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

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