lim-x-0-x-1-x-

Question Number 58239 by salahahmed last updated on 20/Apr/19

\lim_{x \to 0^{+}} (x^{\frac{1}{x}})

Answered by salahahmed last updated on 23/Apr/19

\lim_{x \to 0^{+}} (e^{\frac{\ln (x)}{x}})

e^{\lim_{x \to 0^{+}} (\frac{\ln (x)}{x})}

e^{\lim_{x \to 0^{+}} (\ln (x) \times \frac{1}{x})}

e^{\ln (0^{+}) \times \frac{1}{0^{+}}}

e^{\infty (- \infty)}

e^{- \infty} = 0

∴ \lim_{x \to 0^{+}} (x^{\frac{1}{x}}) = 0