Computing with power series Consider the following function and its power series:
\(f(x)=\frac{1}{(1-x)^{2}}=\sum_{k=1}^{\infty} k x^{k-1}\), for -1 < x < 1.
a. Let \(S_{n}(x)\) be the first n terms of the series. With n = 5 and n = 10, graph f(x) and \(S_{n}(x)\) at the sample points x = -0.9, -0.8,..., -0.1, 0, 0.1,...,0.8, 0.9 (two graphs). Where is the difference in the graphs the greatest?
b. What value of n is needed to guarantee that \(\left|f(x)-S_{n}(x)\right|<0.01\) at all of the sample points?
2/13/15 Principles of Micro-Economics Notes: Supply and Demand (Valentines Edition) Demand The Law of Demand: as price increases, quantity demand falls. LIKEWISE, as price decreases, quantity demand increases. (With Ceteris Paribus: all other variables held constant) Quantity Demand: total amount of goods and services that are demanded and is determined at any given point along the demand curve. (Price v. Quantity graph) Example 1: During Valentines Weekend, prices in plane tickets increase because of all the long distance couples want to see each other. Therefore, single people who just want to travel or go on vacation, are more likely to choose the less expensive route like driving or staying home with Netflix. The quantity of plane tickets that you demand decreases to zero because the price has increased. Example 2: When Valentines Day chocolates go on sale on Feb. 15 , the quantity that you demand increases because the price has fallen. Market Demand: 1. Horizontal Summation 2. How much people are willing and able to buy at any price 3. Negative relationship between price and quantity Normal Goods: When a person’s income increases, demand increases OR when income decreases, demand decreases. (more expensive goods) Example: When your boyfriend gets put into the manager position and hi
