# 007B Sample Midterm 1

**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

Let .

(a) Compute the left-hand Riemann sum approximation of with boxes.

(b) Compute the right-hand Riemann sum approximation of with boxes.

(c) Express as a limit of right-hand Riemann sums (as in the definition of the definite integral). Do not evaluate the limit.

## Problem 2

A population grows at a rate

where is the population after months.

(a) Find a formula for the population size after months, given that the population is at

(b) Use your answer to part (a) to find the size of the population after one month.

## Problem 3

Evaluate the following integrals.

(a)

(b)

## Problem 4

Evaluate the following integrals.

(a)

(b)

## Problem 5

Find the area bounded by and from to

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