limlimits_{x rightarrow 0}left(frac{3 x^{2}+2 | vedclass

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(D) The limit is of the form $1^{\infty}$.Using the formula $\lim_{x 	o a} [f(x)]^{g(x)} = e^{\lim_{x 	o a} [f(x)-1]g(x)}$,we have:Required limit $=

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$e^{-2}$

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(D) The limit is of the form $1^{\infty}$.Using the formula $\lim_{x 	o a} [f(x)]^{g(x)} = e^{\lim_{x 	o a} [f(x)-1]g(x)}$,we have:Required limit $= e^{\lim_{x 	o 0} \left(\frac{3x^2+2}{7x^2+2} - 1ight) \cdot \frac{1}{x^2}}$$= e^{\lim_{x 	o 0} \left(\frac{3x^2+2 - (7x^2+2)}{7x^2+2}ight) \cdot \frac{1}{x^2}}$$= e^{\lim_{x 	o 0} \left(\frac{-4x^2}{7x^2+2}ight) \cdot \frac{1}{x^2}}$$= e^{\lim_{x 	o 0} \left(\frac{-4}{7x^2+2}ight)}$$= e^{\frac{-4}{0+2}} = e^{-2} = \frac{1}{e^2}$

$\lim\limits_{x \rightarrow 0}\left(\frac{3 x^{2}+2}{7 x^{2}+2}\right)^{\frac{1}{x^{2}}}$ is equal to

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