Mathematica Question 1. Do the same for f (x) = Ex and a $. Plot graphs on the i
ID: 3198749 • Letter: M
Question
Mathematica Question1. Do the same for f (x) = Ex and a $. Plot graphs on the interval [-5, 5]- (please make sure your print has four figures, othervise, you have to reduce the size of each figure) Clear [f, x, a, P1, P2, P3, P4); («Use Clear command because it's agood habit*) a=0 P1[x1 ftal +f [al (x-a) f [al f Ial frt tal 2 ftl ta] P3(x-] = f [a] + f' [a] * (x-a fta] f[a] * (x-a), 2 * (x-a) P4 [x_1 = f [a] + f. [a] * (x-a) + 1 + x 234 Plot [ (P1 [x], P2 [x], P3[x], PA[x], f(xl), x, 5, 5), Plotstyle ? {Red, Black, Orange, Blue, {Purple, Thick)), Epilog ? {Pointsize [O.02], Point [ {a, f [a]), Text ["(1,1)", {1.0, 1.2)))] 40 20
Explanation / Answer
When we are iterating the function E^x, for each iteration, the differential function will be divided by it order's factorial.
For example for in P3[x_]=f[a]+ f'[a] *(x-a)/ 1! + f''[a]*(x-a)^2/2! + f'''[a]*(x-a)^3/3!
i.e
P3[x_]=f[a]+ f'[a] *(x-a)/ 1 + f''[a]*(x-a)^2/2 + f'''[a]*(x-a)^3/6.
By plotting this on grpah will show the desired curve.