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Calculus Level 3

Given that f(x)=a0+a1x+a2x2++anxnf(x) = a_0 + a_1 x + a_2 x^2 + \ldots + a_n x^n , and f(x)ex11 |f(x) | \leq | e^{x-1} - 1 | for all x0x \geq 0 . Find the value of yy if ya1+2a2+3a3++nan y \geq |a_1 + 2a_2 + 3a_3 + \ldots + n a_n | .


This is a past-year IIT-JEE problem.
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