Consider the fourier sine series of each of the following functions. in this exercise do not compute the coefficients but use the general convergence theorems (theorems 2, 3, and 4) to discuss the convergence of each of the series in the pointwise, uniform, and l2 senses.(a) f (x) = x3 on (0, ) f (x) = lx − x2 on (0, ) f (x) = x−2 on (0, l).

2.12 school absences. data collected at elementary schools in dekalb county, ga suggest that each year roughly 25% of students miss exactly one day of school, 15% miss 2 days, and 28% miss 3 or more days due to sickness.61 (a) what is the probability that a student chosen at random doesn’t miss any days of school due to sickness this year? (b) what is the probability that a student chosen at random misses no more than one day? (c) what is the probability that a student chosen at random misses at least one day? (d) if a parent has two kids at a dekalb county elementary school, what is the probability that neither kid will miss any school? note any assumption you must make to answer this question. (e) if a parent has two kids at a dekalb county elementary school, what is the probability that both kids will miss some school, i.e. at least one day? note any assumption you make.