Homework Help: Evaulating Limit Question

1. Oct 17, 2011

appplejack

1. The problem statement, all variables and given/known data
Evaluate the limits
lim x->2 f(x) if f(x) = 3, x an integer, or 1, otherwise.

2. Relevant equations

3. The attempt at a solution
I just 3 was the answer because I thought 2 is an integer and if x is an integer then the answer is 3. I was rather shocked to find that the answer is 1. I understand the definition of limits but I think I'm obviously mistaken about something. Thanks.

2. Oct 17, 2011

SammyS

Staff Emeritus
If you're shocked by that limit, then it's clear that you don't understand the definition of limits.

3. Oct 17, 2011

vela

Staff Emeritus
What is your intuitive understanding of what a limit is, appplejack?

4. Oct 17, 2011

appplejack

lim x->c f(x)=L
as 'x' approaches c 'a number' from both sides (-,+) and F(x)= approaches L from both side (-,+).

Last edited: Oct 17, 2011
5. Oct 17, 2011

Dick

That's about right. But the definition of a limit doesn't say anything about the value of f(c) does it? It just talks about the value of f(x) where x is 'close to c'. Not equal to c.