Introduction to Limits: Videos & Practice Problems

Consider the following limit statement and use the definition of infinite right-hand limit to determine a suitable $\delta$ in terms of $B$ that will ensure $\frac{1}{x-4}>B$ whenever $4<x<4+\delta$.
$\underset{x\to 4^{+}}{\lim }\frac{1}{x-4}=\infty$
Definition of infinite right-hand limit:
Suppose that an interval $(c,d)$ lies in the domain of $f$. We say that $f\left(x\right)$ approaches infinity as $x$ approaches $c$ from the right, and write $\underset{x\to c^{+}}{\lim }f\left(x\right)=\infty$, if, for every positive real number $B$, there exists a corresponding number $\delta >0$ such that $f\left(x\right)>B$ whenever $c<x<c+\delta$.