(1 - x2) y" - xy' toy =0 ( * ) where o is a constant. (This equation is important in numerical analysis. I'll explain its meaning in the solutions.) (a) Let's seek a power series solution y = _, and" to (*). First find a recurrence relation between the coefficients a, of the power series solution. (b) Using the recurrence relation from Part (a), compute the coefficients an for n = 2,3, 4, 5, 6, 7 and identify a pattern for an. (You do not need to justify the pattern by induction.) (c) Using your answer to Part (b), find a fundamental set of solutions to (*) expressed as a power series. Justify your answer. (Hint: You can refer to Theorem 5.3.1.) (d) Using your answer to Part (c), show that if o is a non-negative integer, then there is a solution to (*) which is a polynomial of degree a.Uber is a ride-sharing business which is revolutionizing the taxi-market. First, make sure you understand how Uber works by going to their website (Uber.com) and their competitors (Lyft and Sidecar). Then answer the following questions: http://www.economist.comews/finance-and-economics/21599766-microeconomics-ubers-attempt- revolutionise-taxi-markets-pricing-surge http://economicstudents.com/2014/08/the-economics-of-uber/ http://www.bruegel.orgc/blog/detail/article/1445-the-economics-of-uber/ http://www.nytimes.com/2015/06/28/upshot/in-an-uber-world-fortune-favors-the-freelancer.html?_r=0 1. Explain the economics of the taxi medallion system. This is discussed in the text and in numerous places on the web. Why did cities start the medallion system? Do you think it is a good idea? 2. Explain the economics of the ride-sharing firms such as Uber. There's a lot of resources on the web, such as: 3. Should government regulate Uber? Explain your answer.Suppose 79% of voters in a rural area vote on advanced voting days. A random sample of 39 voters is selected. Assuming independence, use the binomial formula or software (recommended) to answer the following questions. Report probabilities accurate to at least 4 decimal places. What is the probability that, of the 39 voters selected: a) exactly 30 vote on advanced voting days? b) exactly 10 do not vote on advanced voting days? c) all of them vote on advanced voting days? d) no less than 26 vote on advanced voting days? e) no more than 27 vote on advanced voting days? f) at least 26 and at most 27 vote on advanced voting days?Use a 1tr'enn diagram to help answer this question. A survey of 120I sophomores at Ball State University showed that: 48 students took economics, 54 took marketing, and 10 took both. What is the percentage of students who did not take either economics or marketing? Show your Venn diagram. 1. Suppose an economy's real GDP is $30,000 in year 1 and $31,600 in year 2. What is the growth rate of its real GDP? Assume that population was 100 in year 1 and 102 in year 2. What is the growth rate of GDP per capita? (Show ALL of your calculations!) 2. When and where did modern economic growth first happen? What are the major institutional factors that form the foundation for modern economic growth? 3. What are the determinants of economic growth? Be sure to identify the type of factor. 4. How is economic growth defined? 5. Why is economic growth important? 6. What are the main sources of economic growth
