1. (07.03 MC) Use Euler's Method with two equal steps to approximate y(1) to three decimal places given the differential equation dy = dx and the initial condition y(0) = 1. (1 point) 9.389 2.559 3.000 95.249 2. (07.03 MC) Given the differential equation = g(x,y) and initial condition g(0) = 1, Euler's Method produces the value y1 = 1 + h . g(0, 1), dx where h equals the step size. Find y2. (1 point) O y2 = 1 + h . g(0, 1) + (h + 1) . g(h + 1, 1 +h . g(0, 1)) O y2 = 1 + h . g(0, 1) + h . g(0, 1) O y2 = 2+h . g(0, 1) + h . g(h, 2 + h . g(0, 1)) O y2 = 1 + h . g(0, 1) + h . g(h, 1 + h g(0, 1))AH Changes savecr 3. (07.03 MC) How does the solution curve produced using Euler's Method for the differential equation % = f(x_y) compare with the actual curve when To(yn_1 +f(X,,_1.yn_1}AX)? (1 point) 0 The solution curve mimics the actual curve perfectly. O The solution curve is shifted Ax units right. 0 The solution curve roughly approximates the actual curve. 0 The solution curve does not approximate the actual curve. 4. (07.03 MC) Let y = f(x) be a solution to the differential equation = x+ y with the initial condition f(0) = m, where m is a constant. Using the initial condition and Ax = 1, Euler's Method gives the approximation f(2) =2 5. Find the value of m. (1 point) 25. (07.03 MC) Find the missing values in the chart below: (1 point) 1 _ o_5_1=__ 0 o 1 1 ( ) 2 1 1 1 1 D.5(i).2'5)=1 2 2 4 8 3 1 1 0.5 0.125 = 2 A a 8 i i 16 3 E l 3 (1.5013125):3 2 16 16 32 4 2 B O A =1 and :1