Name:    MAT 145 Chapter 5 Test (4.9 and 5.1-5.4)

Free Response

1.

Use the given graph of f to find the Riemann sum with six subintervals. Take the sample points to be left endpoints.

2.

Approximate the area under the curve from 0 to using ten approximating rectangles of equal widths and right endpoints.

3.

Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints.

4.

If , find the Riemann sum with correct to 3 decimal places, taking the sample points to be midpoints.

5.

The velocity function (in meters per second) is given for a particle moving along a line. Find the distance traveled by the particle during the given time interval.

6.

If and , find .

7.

Find the area of the region that lies under the given curve.

Round the result to the nearest thousandth.

8.

Evaluate the integral by interpreting it in terms of areas.

9.

Express the sum as a single integral in the form

10.

Find the derivative of the function.

11.

Evaluate the integral if it exists.

12.

Evaluate the integral.

13.

The marginal cost of manufacturing x yards of a certain fabric is (in dollars per yard). Find the increase in cost if the production level is raised from 500 yards to 3,000 yards.

14.

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find a lower estimate for the distance that she traveled during these three seconds.

 t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 4.5 8.4 12.1 13.2 13.3 13.8

15.

The velocity graph of a braking car is shown. Use it to estimate to the nearest foot the distance traveled by the car while the brakes are applied.

Use a left sum with .

16.

Evaluate the Riemann sum for with four subintervals, taking the sample points to be right endpoints.

17.

Evaluate the integral by interpreting it in terms of areas.

18.

Find the interval on which the curve is concave downward.

19.

An animal population is increasing at a rate of per year (where t is measured in years). By how much does the animal population increase between the fourth and tenth years?

Multiple Choice
Identify the choice that best completes the statement or answers the question.

20.

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.