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Question Number 211812 by mokys last updated on 21/Sep/24

$$prove\underset{x\to \mathrm{\infty }}{lim}{(1+\frac{5}{x})}^{\frac{1}{x}}-1=5$$

Commented by mr W last updated on 22/Sep/24

$$wrong!$$$$theresultshouldbe0.$$

Answered by mathmax last updated on 23/Sep/24

$${(1+\frac{5}{x})}^{\frac{1}{x}}\sim 1+\frac{5}{x^2}\Rightarrow {(1+\frac{5}{x})}^{\frac{1}{x}}-1\sim \frac{5}{x^2}(x\to +\mathrm{\infty })\Rightarrow$$$${lim}_{x\to +\mathrm{\infty }}{(1+\frac{5}{x})}^{\frac{1}{x}}-1=0$$

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