I'm not understanding the definition. For any epislon > 0, there exists a delta > 0, st if x belongs to A and 0 < |x - c| < delta, then |f(x) - L| < epsilon.(adsbygoogle = window.adsbygoogle || []).push({});

ok, so to solve a problem, it means that I assume that epsilon is greater then 0, and then, depending on the problem I need to pick a delta that is greater then 0, and it has to satisfy the 0 < |x - c| < delta....and then, it will satisfy |f(x) - L | < epsilon right?

I"m not quite understanding it. So here is the example from book

prove that the lim b from x to c = b.

So first, the book picks f(x) = b. So for any epislon > 0, they let delta be 1. this means if 0 < | x - c | < 1, then |f(x) - b| = |b - b| = 0, which is < epislon.

I dont follow this quite. how/why did they choose f(x) = b? I know it makes sense because b - b = 0, and then it is less then epsilon, so QED, but doesn't it mean you can do the same thing to all limits?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused about limit of function

**Physics Forums | Science Articles, Homework Help, Discussion**