Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Discrete mathematics, continuous mathematics and probability / 3 / a

As $x\to +\infty$, big O notation meansThe same constant must work on the entire sufficiently large tail. Absolute values accommodate signed functions. A two-sided convention at infinity would replace $x\ge x_0$ by $|x|\ge x_0$; the positive-integer arguments in the later parts use the positive-tail convention.