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Arbitrarily close points

Source: Tournament of Towns,Spring 2002, Senior A Level, P2

May 14, 2014

limitalgebra solvedalgebra

Problem Statement

Does there exist points

A,B

on the curve

y=x^3

and on

y=x^3+|x|+1

respectively such that distance between

A,B

is less than

\frac{1}{100}