Determine-i-lim-a-a-1-a-ii-lim-a-0-a-1-a-

Question Number 1766 by Rasheed Ahmad last updated on 18/Sep/15

D e t e r m i n e

(i) \underset{a \to \infty}{l i m} a^{\frac{1}{a}} (i i) \underset{a \to 0}{l i m} a^{\frac{1}{a}}

Answered by 123456 last updated on 19/Sep/15

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

\ln L = \lim_{x \to + \infty} \frac{1}{x} \ln x (\to 0 \infty)

\ln L = \lim_{x \to + \infty} \frac{\ln x}{x} (\to \frac{\infty}{\infty}) L^{'} hospital

\ln L = \lim_{x \to + \infty} \frac{1}{x} = 0

L = 1

- - - - - - - - - - -

D = \lim_{x \to 0^{+}} x^{\frac{1}{x}}

\ln D = \lim_{x \to 0^{+}} \frac{1}{x} \ln x (\to + \infty \times - \infty)

\ln D = - \infty

D = 0

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