Use the Runge-Kutta Fehlberg Algorithm with tolerance TOL = 10~4 to approximate the solution to the following initial-value problems. a. y'= (y/r)2 + y/r, 1 < f < 1.2, y(l) = 1, with/rmax = 0.05 and Amr'n = 0.02. b. y' = sin r + e~', 0 < r < I, y(0) = 0, with hmax 0.25 and hmin 0.02. c. y' = (y2 -f y)/r, 1 < t < 3, y(l) = 2, with hmax = 0.5 and hmin = 0.02. d. y' = t 2 , 0 < / < 2, y(0) 0, with hmax = 0.5 and hmin = 0.02.

MATH 1220 Notes for Week #12 4 April 2016 ● Realize you can bound cos(nx) where n is a positive integer above and below by [1,− 1] ● Then this is bounded on [− R, R] when R = 1 cos(nx) ● Let fn(x) = n on [− R, R], R > 0; can you bound f (x) |nrom|above ● Let M ne the upper bound; since cos(nx) is bounded above by 1 , cos2nxshould be n 1 bounded above by M = n n2 ∞ ● Does ∑ 2 converge n=1n ● Took bad notes this day, but it was mostly just a setup for the other days’ notes; you should get enough i