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Calculus Level 3

Given that \(f(x) = a_0 + a_1 x + a_2 x^2 + \ldots + a_n x^n \), and \( |f(x) | \leq | e^{x-1} - 1 | \) for all \(x \geq 0 \). Find the value of \(y \) if \( y \geq |a_1 + 2a_2 + 3a_3 + \ldots + n a_n | \).


This is a past-year IIT-JEE problem.
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