1. For a special case, show that theImproved Euler’s Method may be referred to as the Trapezoid Rule.Support this claim by writing and solving an example problem usingboth methods.      Â
2. The error associated with Euler'sMethod is proportional to step size. Euler's method will yielderror-free prediction for a certain condition. What is thecondition? Support the claim.
3. Use the Taylor Series to show thatthe Improved Euler’s Method and Midpoint Method have the same orderof accuracy, which is greater than the order of accuracy forEuler’s Method.
4. Use the forward finite differenceapproximation to derive Euler’s formula.
