Chapter 2.7, Problem 60E

Definition of an infinite limit We write $\underset{x\to a}{\lim }f(x)=-\infty$ if for any negative number M there exists δ > 0 such that

$f(x)<Mwhenever0<|x-a|<\delta .$

Use this definition to prove the following statements.

48. $\underset{x\to 1}{\lim }\frac{-2}{{(x-1)}^2}=-\infty$