Question

How do I solve this? My math teachers key says that it is 1 but I’m not sure how he got that.

Answer 1

Given:

$\lim_{x\to-1}(\sqrt[3]{x}-\frac{2}{\sqrt[3]{x}})^5$

You need to substitute this value of "x" into the expression inside the parentheses, in order to evaluate the limit:

$x=-1$

Then:

$\lim_{x\to-1}(\sqrt[3]{-1}-\frac{2}{\sqrt[3]{-1}})^5$

By definition:

$\sqrt[3]{-1}=-1$