- #1

greg_rack

Gold Member

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- Homework Statement
- ##\lim_{x \to +\infty}(\sqrt[3]{x^3-4x^2}-x)##

- Relevant Equations
- none

Hi guys, I am having difficulties in solving this limit.

Below, I'll attach my procedure which ends up in the indeterminate form ##0\cdot \infty##...

How could I solve it?

$$\lim_{x \to +\infty}(\sqrt[3]{x^3-4x^2}-x) \rightarrow

\lim_{x \to +\infty}(x\sqrt[3]{1-\frac{4}{x}}-x) \rightarrow

\lim_{x \to +\infty}[x(\sqrt[3]{1-\frac{4}{x}}-1)]$$

Below, I'll attach my procedure which ends up in the indeterminate form ##0\cdot \infty##...

How could I solve it?

$$\lim_{x \to +\infty}(\sqrt[3]{x^3-4x^2}-x) \rightarrow

\lim_{x \to +\infty}(x\sqrt[3]{1-\frac{4}{x}}-x) \rightarrow

\lim_{x \to +\infty}[x(\sqrt[3]{1-\frac{4}{x}}-1)]$$