## Idealist Group Title Determine lim x approaches 1 f(x) if f(x)=3-x, x doesn't equal to 1 and 1, x=1. one year ago one year ago

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1. KingGeorge Group Title

A good way to see this, is to graph it. |dw:1353365544506:dw|

2. KingGeorge Group Title

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.

3. Idealist Group Title

So the answer would be it doesn't exist, right?

4. KingGeorge Group Title

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.

5. KingGeorge Group Title

Now, since both one-sided limits equal 2, we have that $\lim_{x\to1} f(x)=2.$This is despite the fact that $$f(1)\neq 2$$.

6. Idealist Group Title

Thanks.

7. KingGeorge Group Title

Did that all make sense to you?