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Right Hand Derivative

limx →∞ x2+1x...

Question

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

A

e

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B

1 / e

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C

e^{2}

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D

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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Right Hand Derivative

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