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Single Point Continuity

limn →∞n2 - n...

Question

$lim n \to \infty {(\frac{n^{2} - n + 1}{n^{2} - n - 1})}^{n (n - 1)}$ is equal to

A

e

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B

e^{2}

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C

e^{- 1}

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D

1

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Solution

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

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Single Point Continuity

Standard XII Mathematics

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