MathDB

Problem 3

Part of 1998 VJIMC

Problems(2)

functions converge ptwise to 0, not uniformly convergent

Source: VJIMC 1998 1.3

8/1/2021
Give an example of a sequence of continuous functions on R\mathbb R converging pointwise to 00 which is not uniformly convergent on any nonempty open set.
functioncontinuityreal analysislimitscollege contests
complex roots satisfy |z|>1

Source: VJIMC 1998 2.3

8/24/2021
Show that all complex roots of the polynomial P(z)=a0zn+a1zn−1+…+an−1z+anP(z)=a_0z^n+a_1z^{n-1}+\ldots+a_{n-1}z+a_n, where 0<a0<…<an0<a_0<\ldots<a_n, satisfy ∣z∣>1|z|>1.
algebrapolynomialcomplex numbers