The limit at infinity $\underset{x}{lim}f(x)=L$ means that for any $>0,$ there exists $N>0$ such that $|f(x)-L|<$ whenever $x>N.$ Use the definition of a limit at infinity to prove the statement $\underset{x}{lim}\frac{7x+6}{x}=7$ State the steps for proving that $\underset{x}{lim}f(x)=L.$ Let $$ and $N$ be arbitrary positive numbers. Use the inequality $$ to find a condition of the form $$ where $$ depends only on the value of $$