Download Math 106A Quiz 2: Fall 2011 - Distance Estimation & Minimum n for Integral Approximation and more Exercises Calculus in PDF only on Docsity!
Name:
Math 106A: Fall 2011
Quiz 2: September 23
Please write your final answer in the space provided. For full credit you must show your work. Good Luck!
- The graph below depicts the velocity (in mph) of a bike over a period of 10 hours. The distance traveled by the car in those 10 hours can be calculated by finding the area under the curve. Use the trapezoid rule with 5 intervals (i.e., n = 5) to estimate the distance traveled.
0 2 4 6 8 10
5
10
15
20
25
30
t = time (hours)
v(t)
= velocity (mph)
OVER
- Recall the formulas: |I − Ln| ≤
K 1 (b − a)^2 2 n
|I − Rn| ≤
K 1 (b − a)^2 2 n
|I − Tn| ≤
K 2 (b − a)^3 12 n^2
|I − Mn| ≤
K 2 (b − a)^3 24 n^2
Let I =
− 1
f (x)dx. Below are two graphs. The one on the left is a graph of f ′(x). The one on the
right is a graph of f ′′(x).
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
1
2
3 f '(x)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4
1
2
3 f ''(x)
What is the smallest value of n that guarantees |I − Mn| ≤ 0. 001? (2)
