### Home > CALC > Chapter 5 > Lesson 5.2.5 > Problem 5-104

5-104.

Let

*f*(*x*) =*x*^{1/3}. Homework Help ✎Use the formal definition of continuity to determine if

*f*(*x*) is continuous at*x*= 0.Calculate

. What does the limit in part (b) represent?

What is happening graphically on

*f*(*x*) at*x*= 0 that causes your answer to part(b)?

This is Ana's definition of the derivative. The limit is equivalent to *f* '(0).So you can use the power rule to find the limit, if it exists.

Refer to the hint in part (b).

Recall that derivatives do not exist at locations where *f*(*x*) has a: cusp, endpoint, jump, hole or vertical tangent.

Sketching the graph may help visualize the issue.