1. Using Euler's Method, solve the following with indicated conditions. a y=1+(t-y)2,2st3, use: y(2)-1, with h=0.5, 0.25, and 0.10 b. Assume that y'(t)=4cost-7(t-4) is the solution to some initial value problem on y = 2 when t= Taylor's Series 1 use h=0.2, compute y when t = 3s. 1. f(x)=cos(4x) using x0 = 0 use 8th order Taylor's Series at x = 0.5 2. f(x)=x ex using xo = 0 use 6th order Taylor's Series at x = 1.2 3. f(x) = ex using x0 = 0 use 5th order Taylor's Series at x = 0.2 4. f(x)=ln(3+4x) using x0 = 0 use 7th order Taylor's Series 5. f(2)=7x+using x0 = 1 use 5th order Taylor's Series.