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3

f[x_] := x + 2; g[x_] := Sin[x]; Plot[{f[x], g[x]}, {x, 0, Pi/2}, PlotRange -> {-0.1, 3.65}, PlotLegends -> "Expressions", Filling -> (1 -> {2}), Frame -> True, Epilog -> {Directive[Thick, Magenta], Line[{{#, g[#]}, {#, f[#]}}] & /@ {0, Pi/2}}] rgn = ImplicitRegion[g[x] <= y <= f[x] && 0 <= x <= ...

2

A methode i like to use and a starter. Please see Bisection method and Bisection, in particular: Let $a_n$ and $b_n$ be the endpoints at the nth iteration (with $a_1=a$ and $b_1=b$) and let $r_n$ be the nth approximate solution. Then the number of iterations required to obtain an error smaller than epsilon is found by noting that ...

6

This question was largely dealt with in the comments. I post this for illustrative purposes (but mainly fun): The following shows use of PoissonProcess and its use with RandomFunction, Expectation, Probability. The last line is probability at t=6 that there had been only 1 customer for rate 5/hour: pp = PoissonProcess[5]; rf = RandomFunction[pp, {0, 6}, ...

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