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`