prove-lim-x-1-5-x-1-x-1-5-

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

p r o v e \underset{x \to \infty}{l i m} {(1 + \frac{5}{x})}^{\frac{1}{x}} - 1 = 5

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

w r o n g!

t h e r e s u l t s h o u l d b e 0 .

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 + \infty) \Rightarrow

{l i m}_{x \to + \infty} {(1 + \frac{5}{x})}^{\frac{1}{x}} - 1 = 0

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