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

  1. Let f(x) = x1/3. Homework Help ✎

    1. Use the formal definition of continuity to determine if f(x) is continuous at x = 0.

    2. Calculate .

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

    4. 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.