# 3.5: Limits, Continuity, and Differentiability

- Page ID
- 106352

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This optional summary video from the textbook author might be helpful to use as a preview. Other, more detailed, supplemental videos for this section are posted at the end of the text.

## Supplemental videos

**Homework Exercises 3.5**

### WeBWorK Problems:

**Written Problems:**

**1.**

**2. **Sketch an example of a graph of a function for each of the following descriptions. If such a function is not possible, explain why.

**a. ***f* is continuous at *a* = 2, but is not differentiable at *a* = 2.

**b. ***g* is differentiable at *a* = 3, but does not have a limit at *a* = 3.

**c. ***h* has a limit at *a* = -2, is defined at *a* = -2, but is not continuous at *a* = -2.

**d. ***p*(-1) = 3, \(\lim_{x \to -1} p(x) = 2\)

**e. ***r*(0) = 1, *\(r'(0)=0\)*

**f**. \(\lim_{x \to 1} q(x) = q(1)\) and \(q'(1)\) DNE.