Arija A.'s Microblog - post #225

yall might this problem fun

im struggling with my upper-highschool-levels of maths knowledge, i dont think theres any way i can merge infinite integrals so im looking for online things

Sliding Average Consider a function f(x) that is equal to 1 in the interval x ∈ [-1; 1] and 0 elsewhere: [f(x) graph] Now define a new function g(x). g(x) goes over the entire real line of f(x) in a sliding window of width 1 and, at each point of f(x), takes the average of all values in that sliding window, creating a new graph.  On first iteration of g(x) this graph is an even-sided trapezoid: [g(x) graph] Now repeat this process: let f(x) = g(x) and continue taking the sliding window average an infinite amount of times.  Which function h(x) best describes the final function f(x) after n iterations of g(x) as n approaches infinity?

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