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At 02:08, this video shows a function that grows from exactly 0 at input x = 0+, up to 1 at ##x=\infty##.
Its value and all its derivatives approach 0 as x -> 0. The function is Exp(-1 / x^2).
www.youtube.com/watch?v=Wwg_15a0DJo&t=146s
Q. : What function would have its value and all derivatives = 0 at 0+, then grow with x and attain a value of unity at x -> 1- with all derivatives also tending to zero as x -> 1- ?
Its value and all its derivatives approach 0 as x -> 0. The function is Exp(-1 / x^2).
www.youtube.com/watch?v=Wwg_15a0DJo&t=146s
Q. : What function would have its value and all derivatives = 0 at 0+, then grow with x and attain a value of unity at x -> 1- with all derivatives also tending to zero as x -> 1- ?