$$\displaystyle \lim_{x \to \infty} x^{1/x}$$ It's supposed to be calculated with L´Hospital rules, but I can´t find the way of express the limit as a quotient.
2026-03-28 23:57:53.1774742273
Limit $\lim\limits_{x \to \infty} x^{1/x}$
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EDIT since the question changed: $x^{1/x} = e^{\log(x^{1/x})} = e^{\frac{\log x}{x}}$. Then you have:$$\lim_{x \to \infty}x^{1/x} = \lim_{x \to \infty}e^{\frac{\log x}{x}} = e^{\lim_{x \to \infty}\frac{\log x}{x}} = 1,$$ where the last equality follows noticing that $\lim_{x \to \infty}\frac{\log x}{x} = 0$.