Math 161

Sample 3rd Midterm

Dr. Wilson

 

1. An object's velocity is measured as a function of time.

2.

Let

Sketch the graph of F(x) over the interval (a , b).

3. Given

Find formulas for v(t) and y(t). Include your constants of integration. Interpret these constants of integration.

Using these formulas, find when a water balloon which is launched upward with an initial velocity of 50ft/sec from the top of a stadium, which is 40ft above the ground, hits the ground. What is its velocity when it hits the ground?

4. The rate at which the population of a town is increasing is 3% per year. i.e.,

where the population, P, is measured in people and the time, t, is measured in years.

Solve this differential equation to get the population as a function of time. If we start measuring the time now (i.e., t = 0 at the present) and the population of the town is 30,000 people now, what will the population be in 5 years?

5. Find the following indefinite integrals. 5a, 5b, 5c, 5d.

6. Find the following definite integrals.

6a, 6b, 6c, 6d.