Chapter 2.7, Problem 65E

Definition of a limit at infinity The limit at infinity $\underset{x\to \infty }{\lim }f(x)=L$ means that for any ε > 0 there exists N > 0 such that

$|f(x)-L|<\epsilon wheneverx>N.$

Use this definition to prove the following statements.

51. $\underset{x\to \infty }{\lim }\frac{2x+1}{x}=2$