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

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KingGeorgeBest ResponseYou've already chosen the best response.1
A good way to see this, is to graph it. dw:1353365544506:dw
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
So 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.
 one year ago

IdealistBest ResponseYou've already chosen the best response.0
So the answer would be it doesn't exist, right?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Not 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.
 one year ago

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

KingGeorgeBest ResponseYou've already chosen the best response.1
Did that all make sense to you?
 one year ago
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