lim-x-6x-8x-2-2x-3-4x-5-x-6-x-3-4x-5-1-6-x-

Question Number 130176 by liberty last updated on 23/Jan/21

\lim_{x \to \infty} \frac{6 x + \sqrt{{8 x}^{2} - \sqrt{{2 x}^{3} + \sqrt{{4 x}^{5}}}}}{\sqrt[6]{x^{6} - x^{3} + \sqrt{{4 x}^{5}}} + x} = ?

Answered by EDWIN88 last updated on 23/Jan/21

\lim_{x \to \infty} \frac{6 x + \sqrt{{8 x}^{2} - \sqrt{{2 x}^{3} + {2 x}^{2} \sqrt{x}}}}{\sqrt[6]{x^{6} - x^{3} + {2 x}^{2} \sqrt{x}} + x} =

\lim_{x \to \infty} \frac{6 x + \sqrt{{8 x}^{2} - x \sqrt{2 x + 2 \sqrt{x}}}}{x \sqrt[6]{1 - x^{- 3} + {2 x}^{- 4} \sqrt{x}} + x} =

\lim_{x \to \infty} \frac{x (6 + \sqrt{8 - x^{- 1} \sqrt{2 x + 2 \sqrt{x}}})}{x (\sqrt[6]{1 - x^{- 3} + {2 x}^{- 4} \sqrt{x}} + 1)} =

\frac{6 + \sqrt{8}}{2} = 3 + \sqrt{2}

Facebook Tweet Pin