10 Multiple Choice Sigma Notation and the Summation questions
10 Multiple Choice Sigma Notation and the Summation questions
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)