Limite da divisão das raízes

[Atila]

Como resolver esse limite?
\(\lim_{x\rightarrow \infty } \left |\frac{\sqrt[4]{x}}{\sqrt[4]{x+1}} \right |\)

[danjr5]

Atila, boa noite!

\(\lim_{x \to \infty} \begin{vmatrix}\frac{\sqrt[4]{x}}{\sqrt[4]{x + 1}}\end{vmatrix} =\)

\(\lim_{x \to \infty} \begin{vmatrix}\sqrt[4]{\frac{x}{x + 1}}\end{vmatrix} =\)

\(\lim_{x \to \infty} \begin{vmatrix}\sqrt[4]{\frac{x}{x\left (1 + \frac{1}{x} \right )}}\end{vmatrix} =\)

\(\lim_{x \to \infty} \begin{vmatrix}\sqrt[4]{\frac{1}{\left (1 + \frac{1}{x} \right )}}\end{vmatrix} =\)

\(\begin{vmatrix}\sqrt[4]{\frac{1}{\left (1 + 0 \right )}}\end{vmatrix} =\)

\(|\sqrt[4]{1}| =\)

\(\fbox{1}\)