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B.Stat & B.Math 2022 - Q7

Source: Indian Statistical Institute (ISI) - B.Stat & B.Math Entrance 2022

May 8, 2022

isiIndian Statistical Institute2022polynomiallimit

Problem Statement

Let

P(x)=1+2 x+7 x^{2}+13 x^{3}~,\qquad x \in \mathbb{R} .

Calculate for all

x \in \mathbb{R},

\lim _{n \rightarrow \infty}\left(P\left(\frac{x}{n}\right)\right)^{n}