# 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

To determine drug dosages, doctors estimate a person's body surface area (BSA) (in meters squared) using the formula:

where is the height in centimeters and is the mass in kilograms. Calculate the rate of change of BSA with respect to height for a person of a constant mass of What is the rate at and Express your results in the correct units. Does the BSA increase more rapidly with respect to height at lower or higher heights?

## Problem 5

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

(a)

(b)

(c)

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