If-f-x-8x-3-3x-then-lim-x-x-1-3-f-1-8x-f-1-x-is-

Question Number 132537 by SLVR last updated on 15/Feb/21

I f f (x) = 8 x^{3} + 3 x t h e n {l i m}_{x \to \infty} \frac{x^{1 / 3}}{f^{- 1} (8 x) - f^{- 1} (x)} i s

Commented by SLVR last updated on 15/Feb/21

c a n a n y o n e h e l p m e \dots p l e a s e

Answered by Ñï= last updated on 16/Feb/21

x = 8 t^{3} + 3 t

\lim_{x \to \infty} \frac{f^{- 1} (x)}{x^{1 / 3}} = \lim_{t \to \infty} \frac{f^{- 1} (8 t^{3} + 3 t)}{{(8 t^{3} + 3 t)}^{1 / 3}} = \lim_{t \to \infty} \frac{t}{{(8 t^{3} + 3 t)}^{1 / 3}} = \frac{1}{2}

\lim_{x \to \infty} \frac{f^{- 1} (8 x)}{x^{1 / 3}} = 2 \lim_{x \to \infty} \frac{f^{- 1} (8 x)}{{(8 x)}^{1 / 3}} = 1

\lim_{x \to \infty} \frac{x^{1 / 3}}{f^{- 1} (8 x) - f^{- 1} (x)} = \frac{1}{1 - \frac{1}{2}} = 2

Facebook Tweet Pin