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Math Help - Limits Help

  1. #1
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    Limits Help

    Hi,

    I have just started a calulus class (i'm a high school senior) and we've been introduced to limits.

    I am unsure of how to facor the following

    <br /> <br />
lim (x^2+5x)/(x+4)<br /> <br />
    With the limit approaching zero.
    I factored it to:

    x(x+5)/(x+4)

    and got a limit of zero. Is that the final answer or is there another way to get another value?

    Thanks in advance for your help!
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  2. #2
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    There's actually no need to factor here (although what you did is not wrong). When you substitute 0 in for x you get 0/4 which is 0. So the limit is 0.
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  3. #3
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    Okay thanks.
    I was kind of confused about whether or not the zero was indeed the limit.
    Is the general rule that if you plug in the approaching value and you get 0/0, you have to factor further?
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  4. #4
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    0/c is just 0 as long as c is not 0.

    0/0 is an indeterminate form. More work needs to be done to compute the limit. There isn't one technique that will work all the time, but if you have a rational function (a quotient of polynomials), then the factoring technique you're talking about will always work.
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