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Idealist

  • 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
    • 3 years ago
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    A good way to see this, is to graph it. |dw:1353365544506:dw|

  2. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    So the answer would be it doesn't exist, right?

  4. KingGeorge
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    Thanks.

  7. KingGeorge
    • 3 years ago
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    Did that all make sense to you?

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