Lim_x →∞ (x^2+1x^2 1 )^x^2 =e^lim_x →∞ (x^2+1x^2 1 1 )(x^2) =e^lim_x →∞ (2x^2 1 nbsp; )(x^2) =e^2 ...

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Right Hand Derivative

limx →∞ x2+1x...

Question

$lim x \to \infty {(\frac{x^{2} + 1}{x^{2} - 1})}^{x^{2}} =$

e

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1 / e

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e^{2}

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e^{- 2}

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Solution

The correct option is C $e^{2}$
$lim x \to \infty {(\frac{x^{2} + 1}{x^{2} - 1})}^{x^{2}}$
$= e^{lim x \to \infty ⎛ ⎜ ⎝ \frac{x^{2} + 1}{x^{2} - 1} - 1 ⎞ ⎟ ⎠ (x^{2})}$
$= e^{lim x \to \infty ⎛ ⎝ \frac{2}{x^{2} - 1} ⎞ ⎠ (x^{2})}$
$= e^{2}$

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