# 009A Sample Midterm 2

**This is a sample, and is meant to represent the material usually covered in Math 9A for the midterm. An actual test may or may not be similar.**

**Click on the** ** boxed problem numbers to go to a solution.**

## Problem 1

Evaluate the following limits.

(a) Find

(b) Find

(c) Evaluate

## Problem 2

The function is a polynomial and therefore continuous everywhere.

(a) State the Intermediate Value Theorem.

(b) Use the Intermediate Value Theorem to show that has a zero in the interval

## Problem 3

Use the definition of the derivative to find for the function

## Problem 4

Find the derivatives of the following functions. Do not simplify.

(a)

(b) where

## Problem 5

Find the derivatives of the following functions. Do not simplify.

(a)

(b)

(c)

**Contributions to this page were made by Kayla Murray**