Answer the following problems: 1. In your own words, compare the following (in terms of the concept and error): a. Trapezoidal Rule and Simpson's 1/3 Rule b. Simpson's 1/3 Rule and Simpson's 3/8 Rule 2. Give a particular application (or future research) of the following: a. Romberg Rule b. Gaussian Integrals 3. In your own words, explain the following: a. the concept of ordinary differential equation (ODE) and give a particular application that you may use for your future research. b. the importance of Lipschitz condition. 4. Give an example of an unstable method other than what we have discussed in class and explain it clearly. 5. Given the initial value problem (IVP). y' = f(t,y) y(to) = Wo where f is continuous and real valued on the set U. with (to, yo) E U. Show that if y(t) is a solution for this IVP in an interval it - tol 0.b> 0. and || || is any appropiate norm on R&quot