Evaluate-the-given-limit-lim-n-8-1-n-1-16-1-n-1-

Question Number 203508 by Fridunatjan08 last updated on 20/Jan/24

E v a l u a t e t h e g i v e n l i m i t :

\underset{n \to \infty}{l i m} \frac{\sqrt[n]{8} - 1}{\sqrt[n]{16} - 1}

Answered by esmaeil last updated on 20/Jan/24

= Y

\frac{1}{n} = p \to (n \to \infty \to p \to 0)

\to Y = \lim_{p \to 0} \frac{2^{3 p} - 1}{2^{4 p} - 1} \overset{h o p i t a l}{=} \lim_{p \to 0} \frac{2^{3 p} \times 3 l n 2}{2^{4 p} \times 4 l n 2}

= \frac{3}{4}

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