# AP Calculus: Limits

1. Feb 18, 2005

### Pseudo Statistic

Here's a limit question which I can't seem to figure out how to do, if someone can explain how to do this one question, I'd greatly appreciate it, as I barely understand this:

In Excercise 9, a positive number E and the limit L of a function f at a are given. Find a number DELTA such that |f(x) -L| < E if 0 < |x-a| < DELTA

Excercise 9:
$$\lim_{x \rightarrow 4} 2x = 8; E = 0.1$$

Thanks.

2. Feb 18, 2005

### Galileo

Write down what you know and what you need to prove:

Find a $\delta>0$, such that:
$$|2x-8|<0.1$$ whenever $$|x-4|<\delta$$

That's almost always the first step. Simply write it down. The answer may already be obvious from the above expression.