Chapter 2.7, Problem 53E

Definition of infinite limits at infinity We write $\underset{x\to \infty }{\lim }f(x)=\infty$ if for any positive number M there is a corresponding N > 0 such that

$f(x)>M\text{whenever}x>N.$

Use this definition to prove the following statements.

53. $\underset{x\to \infty }{\lim }\frac{x^2+x}{x}=\infty$