Trying to help my girlfriend since we're both in Calculus this semester, but my class never went this in depth into limit proofs. A little help so I can pass it on? (:
The limit at infinity $\lim_{x\to\infty} f(x) = L$ means that for any $\varepsilon > 0$, there exists $N > 0$ such that
$|f(x) - L| < \varepsilon$ whenever $x > N$.
Use this definition to prove the following statements.
- $\lim\limits_{x \to +\infty} \frac{10}{x} = 0.$
- $\lim\limits_{x \to +\infty} \frac{2x+1}{x} = 2.$
Thanks in advance!