# 007B Sample Midterm 3

**This is a sample, and is meant to represent the material usually covered in Math 7B 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

Divide the interval into four subintervals of equal length and compute the right-endpoint Riemann sum of

## Problem 2

Compute the following integrals:

(a)

(b)

## Problem 3

For a fish that starts life with a length of 1cm and has a maximum length of 30cm, the von Bertalanffy growth model predicts that the growth rate is cm/year where is the age of the fish. What is the average length of the fish over its first five years?

## Problem 4

Find the volume of the solid obtained by rotating the region bounded by and about the axis. Sketch the graph of the region and a typical disk element.

## Problem 5

Evaluate the following integrals.

(a)

(b)

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