16.) You can use technology for this problem, keep calculations accurate to at least 10 decimal places. Consider:

???=????,??(0)=1, ?=0.1.

a.) Using Euler's Method

i.) Summarize the results for the approximation for ??(1) into a table. Include your values of ????, the approximation at each step ????, the exact value ??(????) and the absolute error at each step.

ii.) Plot the graph of the approximation curve and the graph of the exact solution on the same graph.

b.) Using Improved Euler's Method

i.) Summarize the results for the approximation for ??(1) into a table. Include your values of ????, the approximation at each step ????, the exact value ??(????) and the absolute error at each step.

ii.) Plot the graph of the approximation curve and the graph of the exact solution on the same graph.

c.) Using RK4

i.) Summarize the results for the approximation for ??(1) into a table. Include your values of ????, the approximation at each step ????, the exact value ??(????) and the absolute error at each step.

ii.) Plot the graph of the approximation curve and the graph of the exact solution on the same graph.

d.) On a single graph plot the absolute errors at each step, ??, for (a), (b) and (??)

15.} 1I"ou can use technology:r for this problem, keep calculations accurate to at least 1{] decimal places. Consider: y' = army-() = 1, h = {1.1. a.) Using Euler' s Method i.] Summarize the results for the approximation for 3.411) into a table. Include your values of x\