Lim_n →∞ ( 1+sin ( an ) )^n, [1^∞ form] =e^lim_n →∞ n ( 1+sin ( an ) 1 ) = e^lim_n →∞n ( sin ( an ) ) Multiplying and dividing by a = nbsp; e^lim_n →∞s ...

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Standard XII

Mathematics

Continuity of a Function

limn →∞ 1+sin...

Question

$lim n \to \infty {(1 + sin (\frac{a}{n}))}^{n} =$

e

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e^{a}

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a^{e}

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a

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Solution

The correct option is B $e^{a}$
$lim n \to \infty {(1 + sin (\frac{a}{n}))}^{n}, [1^{\infty} form]$
$= e^{lim n \to \infty n (1 + sin (\frac{a}{n}) - 1)}$
$= e^{lim n \to \infty n (sin (\frac{a}{n}))}$
Multiplying and dividing by $a$
$= e^{lim n \to \infty sin (\frac{a}{n}) \times \frac{a}{a / n}}$
$= e^{a}$

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Continuity of a Function

Standard XII Mathematics

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limn→∞(1+sin(an))n=

The correct option is B ealimn→∞(1+sin(an))n, [1∞ form] =elimn→∞n(1+sin(an)−1) =elimn→∞n( sin(an)) Multiplying and dividing by a =elimn→∞sin(an)×aa/n =ea

$lim n \to \infty {(1 + sin (\frac{a}{n}))}^{n} =$