We have, #10; #10; ( x→∞lim ( #10;1+1x)^x)^2 #160; #10; #10;We know that #10; #10; x→∞lim ( 1+1x #10;)^x=e #10; #10; #160;Ther ...

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Existence of Limit

limx →∞ 1 + 1...

Question

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

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Solution

We have,

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

We know that

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

Therefore,

$= e^{2}$

Hence, this is the answer.

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