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2 votes
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Find the value of above limit.

How to approach with  this type of infinity power infinity problems ??

im thinking like first we should convert this to 1 power infinity problem and then solve??

is it correct ?? please solve above que

1 Answer

1 votes
1 votes
$\large \lim_{n\rightarrow \infty} \left ( \frac{2n^{2}}{3n^{2}+1} \right )^{\LARGE \frac{-3n+{2}}{5n^{2}-3}}$

Let n = $\large \frac{1}{t} $

$\large \lim_{t\rightarrow 0} \left ( \frac{\frac {2}{t^{2}}}{\frac {3}{t^{2}}+1} \right )^{\LARGE \frac{\frac {-3}{t} +{2}}{\frac {5}{t^{2}}-3}}$

$\large \lim_{t\rightarrow 0} \left ( \frac{2}{3 + t^{2}} \right )^{\LARGE \frac{t(-3 +{2t})}{5-3t^{2}}}$

$\large \left ( \frac{2}{3 + 0^{2}} \right )^0$

The answer is $ 1$

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