Here's the question you clicked on:
Idealist
Determine lim x approaches 1 f(x) if f(x)=3-x, x doesn't equal to 1 and 1, x=1.
A good way to see this, is to graph it. |dw:1353365544506:dw|
So for every but at the point x=1, you have the function y=3-x. If you look at that graph, tell me what you think the limit will be.
So the answer would be it doesn't exist, right?
Not quite. To find the limit, we need to find the one sided limits first. The limit \[\lim_{x\to1^-} 3-x\]is 2. You should be able to convince yourself of this by looking at a graph of y=3-x. Next, the limit\[\lim_{x\to1^+}3-x\]is also 2.
Now, since both one-sided limits equal 2, we have that \[\lim_{x\to1} f(x)=2.\]This is despite the fact that \(f(1)\neq 2\).
Did that all make sense to you?