Sliding Average
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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?](/pics/image/3209354039b019f3e59e68e53feff20db3f325f6e1818399b595839e0bb89dec)
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