(1 point) Use a linear approximation to estimate the number (27.07) 2/3. Answer: (1 point) Use Euler's method with the given step size to estimate y(1.4) where y(x) is the solution of the initial-value problem y = x - xy, y(1) = 0. 1. Estimate y(1.4) with a step size h = 0.2. Answer: y(1.4) .2*(1+.96) 2. Estimate y(1.4) with a step size h = 0.1. Answer: y(1.4) (1 point) Let y(t) be the solution to y = 5te y satisfying y(0) = 2. (a) Use Euler's Method with time step h = 0.2 to approximate y(0.2), y(0.4), . . ., y(1.0). k tk 00 2 10.2 20.4 30.6 40.8 5 1.0 (b) Use separation of variables to find y(t) exactly. y(t) = (c) Compute the error in the approximations to y(0.2), y(0.6), and y(1). |y(0.2) - y| = |y(0.6) y3 | = |y(1) y5 | =