## anonymous 3 years ago Determine lim x approaches 1 f(x) if f(x)=3-x, x doesn't equal to 1 and 1, x=1.

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1. KingGeorge

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

2. KingGeorge

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. anonymous

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

4. KingGeorge

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

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. anonymous

Thanks.

7. KingGeorge

Did that all make sense to you?