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

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KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1A good way to see this, is to graph it. dw:1353365544506:dw

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1So for every but at the point x=1, you have the function y=3x. If you look at that graph, tell me what you think the limit will be.

Idealist
 3 years ago
Best ResponseYou've already chosen the best response.0So the answer would be it doesn't exist, right?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Not quite. To find the limit, we need to find the one sided limits first. The limit \[\lim_{x\to1^} 3x\]is 2. You should be able to convince yourself of this by looking at a graph of y=3x. Next, the limit\[\lim_{x\to1^+}3x\]is also 2.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Now, since both onesided limits equal 2, we have that \[\lim_{x\to1} f(x)=2.\]This is despite the fact that \(f(1)\neq 2\).

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Did that all make sense to you?
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