To derive euler’s method, we truncated the taylor series expansion of yi+1 at the linear term. we could truncate at the quadratic term instead, giving the so-called taylor method of order 2. this method approximates yi+1 byωi+1= ωi+ hf(ti,ωi) + h^2/2. df/dt| (ti,ωi)a. for the ivp y'(t)= y^2. e^-t, 0 ≤ t ≤ 1, y(0)= 1, calculate df/dt. b. by hand, use both euler's method and the taylor method of order 2 to approximate y(1) with h=0.5