Please make numbers easy to read. Problem is a few parts, A-D. Consider the initial value problem below to answer to following.a) Find the approximations to y(0.4) and y(0.8) using Euler's method with time steps of At = 0.4, 0.2, 0.1, and 0.05.b) Using the exact solution given, compute the errors in the Euler approximations at t=0.4 and t= 0.8.cj Which time step results in the more accurate approximation? Explain your observations.d) In general, how does halving the time step affect the error at t= 0.4 and t= 0.8?y'(t) = 6t + 1, y(0) = 0, y(t) = 3r² +ta) Complete the table below.At Approximation to y(0.4) Approximation to y(0.8)0.40.20.10.05(Round to tive decimal places as needed.)b) Complete the table below.AtErrors for y(0.4)Errors for y(0.8)0.40.20.10.05(Roundfive decimal places as needed.)c) Which time step results in the more accurate approximation?O A. Time step At= 0.4 results in the more accurate approximation because larger time steps generally produce more accurate results.O B. Time step At= 0.4 results in the more accurate approximation because larger time steps generally produce smaller numbers.O C. Time step At=0.05 results in the more accurate approximation because smaller time steps generally produce more accurate results.O D. Time step At = 0.05 results in the more accurate approximation because smaller time steps generally produce smaller numbers.d) How did halving the time step affect the error at t= 0.4 and t= 0.8?O A. Halving the time steps results in approximately doubling the error.B. Halving the time steps results in reducing the error by approximately one tenth.OC. Halving the time steps results in approximately halving the error.O D. Halving the time steps results in reducing the error by approximately one fourth.

Name: Please make numbers easy to read. Problem is a few parts, A-D. Conside
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Please make numbers easy to read. Problem is a few parts, A-D. Consider the initial value problem below to answer to following.a) Find the approximations to y(0.4) and y(0.8) using Euler's method with time steps of At = 0.4, 0.2, 0.1, and 0.05.b) Usi