Basic Analysis I — Real Analysis · Problem 3.5.4

Continuous Functions — Jiri Lebl

Mathematics — Real Analysis · limits-at-infinity

Problem

Let us justify terminology. Let

f : \mathbb{R} \to \mathbb{R}

be a function such that

\lim_{x \to \infty} f(x) = \infty

(diverges to infinity). Show that

f(x)

diverges (i.e. does not converge) as

x \to \infty