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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.

  1. $\lim\limits_{x \to +\infty} \frac{10}{x} = 0.$
  2. $\lim\limits_{x \to +\infty} \frac{2x+1}{x} = 2.$

Thanks in advance!

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    The second is not very different from the first. Have you written down what $f(x) - L$ is in that situation?2011-09-12

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