Name:
Math 106C: Winter 2012
Quiz 1: January 30
Please write your final answer in the space provided. For full credit you must show your work. Good Luck!
1. Let I=Zb
a
f(x)dx, where fis positive and concave down over the interval [a, b]. Indicate whether,
for all n≥1, the statement must be true, cannot be true, or may be true.
(a) Rn≤I(1a)
(b) Tn≤I(1b)
2. The graph below depicts the velocity (in mph) of a bike over a period of 8 hours. The distance
traveled by the car in those 8 hours can be calculated by finding the area under the curve. Use the
Midpoint Rule with 4 intervals (i.e., n= 4) to estimate the distance traveled.
(2)
0 1 2 3 4 5 6 7 8
5
10
15
20
t = time (hours)
v(t) = velocity (mph)
OVER
