isi-entrance 2022 Q7

isi-entrance · India · UGB Taylor series Limit evaluation using series expansion or exponential asymptotics

Let $$P(x) = 1 + 2x + 7x^2 + 13x^3, \quad x \in \mathbb{R}$$ Calculate for all $x \in \mathbb{R}$, $$\lim_{n \to \infty} \left(P\left(\frac{x}{n}\right)\right)^n$$

Let
$$P(x) = 1 + 2x + 7x^2 + 13x^3, \quad x \in \mathbb{R}$$
Calculate for all $x \in \mathbb{R}$,
$$\lim_{n \to \infty} \left(P\left(\frac{x}{n}\right)\right)^n$$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9