The discussion revolves around evaluating limits, specifically the limit as x approaches 2 for a piecewise function defined as f(x) = 3 when x is an integer and f(x) = 1 otherwise. Participants express confusion regarding the application of the limit definition and its implications for the function's value at the point of interest.
The discussion is ongoing, with participants actively questioning assumptions about the limit definition and its application to the given function. Some guidance has been offered regarding the distinction between the limit and the function's value at the point, but no consensus has been reached.
There appears to be a misunderstanding related to the definition of limits, particularly concerning the value of the function at the point of interest versus the behavior of the function as it approaches that point.
If you're shocked by that limit, then it's clear that you don't understand the definition of limits.appplejack said:Homework Statement
Evaluate the limits
lim x->2 f(x) if f(x) = 3, x an integer, or 1, otherwise.
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.
appplejack said:lim x->c f(x)=L
as 'x' approaches c 'a number' from both sides (-,+) and F(x)= approaches L from both side (-,+).