# 10 multiple choice 5 short answers

1.

Use the properties of sigma notation and the summation formulas to evaluate . (5 points)

2.

Let . Use geometric formulas to evaluate . (5 points)

3.

Write the definite integral for the summation: . (5 points)

4.

Find . (5 points)

5.

Find an antiderivative of . (5 points)

6.

Evaluate . (5 points)

7.

Evaluate the integral . (5 points)

8.

Find the antiderivative of . (5 points)

9.

Use your calculator to evaluate . Give 3 decimal places for your answer. (5 points)

10.

Suppose and , find the value of . (5 points)

1.

Using n = 4 equal-width rectangles, approximate . Use the mid-point of each sub-interval to determine the height of each rectangle. (10 points)

2.

Water leaks from a tank at the rate of r(t) gallons per hour. The rate decreased as time passed, and values of the rate at two-hour time intervals are shown in the table below. The total amount of water that leaked out is evaluated by a Riemann sum. Find the upper estimate (left end-points of each rectangle) for the total amount of water that leaked out by using five rectangles.

Give your answer with one decimal place. (10 points)

t (hr) | 0 | 2 | 4 | 6 | 8 | 10 |
---|---|---|---|---|---|---|

r(t) (gal/hr) | 10.7 | 8.6 | 6.6 | 5.2 | 5.0 | 4.5 |

3.

Find the interval on which the curve of is concave up. (10 points)

4.

Evaluate . (10 points)

5.

Evaluate exactly the value of . Your work must include the use of substitution and the antiderivative. (10 points)