Solve the following initial value problem by hand calculation over the interval from t = 0 to t = 2 using the two specified methods. The initial condition is y(0) = 1. dy dt = t²y — 1.1y - The analytic solution to this ODE is y(t) = exp(t³/3- 1.1t). For both solution methods below, make a table of the numerical solution values, the analytic solution values and the percentage error between the numerical and analytic solution at t = 0.5, 1, 1.5. Define the percentage error as follows: Ynum Yanalytic % error = × 100 Yanalytic (a) Using Euler's method with h = 0.5 and h = 0.25. (b) Using the midpoint method with h = 0.5

Complete the following Diagram eo So

Determine the validity of the ff. proof: Theorem: "the sum of any two rational numbers is a rational number" Proof: "Proof: Suppose r and s are rational numbers. By definition of rational, r = a/b for some integers a and b with b + 0, and s = a/b for some integers a and b with b + 0. Then 2a a r+s ==+ b b a - = b Let p = 2a. Then p is an integer since it is a prod- uct of integers. Hence r+s = p/b, where p and b are integers and b + 0. Thus r+ s is a rational number by definition of rational. This is what was to be shown." Maybe O Yes, it is valid Insufficient information to find the answer Not valid

The equation XA + XB = XA+B is always held.  Group of answer choices True False