mathop {lim }limits_{x to 0} frac{{{{(27 + x) | vedclass

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Question

(C) ધારો કે $L = \mathop {\lim }\limits_{x 	o 0} \frac{{{{(27 + x)}^{\frac{1}{3}}} - 3}}{{9 - {{(27 + x)}^{\frac{2}{3}}}}}$$x = 0$ મૂકતા,આપણને $\frac

Vedclass · Accepted Answer

$-\frac{1}{6}$

Vedclass · Answer

(C) ધારો કે $L = \mathop {\lim }\limits_{x 	o 0} \frac{{{{(27 + x)}^{\frac{1}{3}}} - 3}}{{9 - {{(27 + x)}^{\frac{2}{3}}}}}$$x = 0$ મૂકતા,આપણને $\frac{0}{0}$ અનિશ્ચિત સ્વરૂપ મળે છે.એલ-હોસ્પિટલના નિયમનો ઉપયોગ કરતા:$L = \mathop {\lim }\limits_{x 	o 0} \frac{{\frac{d}{{dx}}({{(27 + x)}^{\frac{1}{3}}} - 3)}}{{\frac{d}{{dx}}(9 - {{(27 + x)}^{\frac{2}{3}}})}}$$L = \mathop {\lim }\limits_{x 	o 0} \frac{{\frac{1}{3}{{(27 + x)}^{ - \frac{2}{3}}}}}{{ - \frac{2}{3}{{(27 + x)}^{ - \frac{1}{3}}}}}$$L = \mathop {\lim }\limits_{x 	o 0} -\frac{1}{2} {(27 + x)}^{ - \frac{1}{3}}$$L = -\frac{1}{2} 	imes \frac{1}{3} = -\frac{1}{6}$

$\mathop {\lim }\limits_{x \to 0} \frac{{{{(27 + x)}^{\frac{1}{3}}}} - 3}{{9 - {{(27 + x)}^{\frac{2}{3}}}}}$ ની કિંમત શોધો.

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