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Math Help - Evaluate the limit, if it exists.

  1. #1
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    Evaluate the limit, if it exists.

    hey guys, so I'm doing some limit questions, and I'm kind of stuck on one, and it's a even number so I have no solution for it in the book onto how to do it, but anyways this is what I have for this question so far.

    Question:
    lim (3+h)-1-3-1/ h
    h ->0

    Ok so this is what I've done so far,

    lim 1/(3+h) - 1/3 all divided by h
    h ->0

    lim 3-(3+h)/3(3+h) all divided by h
    h ->0

    lim 3-3-h/9+3h * 1/h
    h ->0


    lim 3-3-1/9+3h (cancelled the h's)
    h ->0


    Plug in the 0s where the h is -1/ 9+3(0) = -1/9,

    Not sure if this is correct or not, and I think I may have made a mistake somewhere, please correct me if so.


    Thank you, sorry if the format isn't as good, I think some of you know I'm terrible with that stuff lol.
    Last edited by Oldspice1212; May 11th 2013 at 01:23 PM.
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  2. #2
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    Re: Evaluate the limit, if it exists.

    Quote Originally Posted by Oldspice1212 View Post
    Question:
    lim (3+h)-1-3-1/ h
    h ->0
    Ok so this is what I've done so far,
    lim 1/(3+h) - 1/3 all divided by h
    h ->0
    lim 3-(3+h)/3(3+h) all divided by h
    h ->0
    lim 3-3-h/9+3h * 1/h
    h ->0
    lim 3-3-1/9+3h (cancelled the h's)
    h ->0

    Plug in the 0s where the h is -1/ 9+3(0) = -1/9,
    All of that is correct except that. We never never plug in when doing limits.
    That is a completely wrong way to think about limits.

    What happens to \frac{(3)-(3+h)}{3h(h+3)} as h\ne 0~\&~x\sim 0~?
    That is, h is 'close to' but not equal to zero. Unless that is clear to you then you will have trouble later on in mathematical proofs.
    Thanks from Oldspice1212
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  3. #3
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    Re: Evaluate the limit, if it exists.

    All of that is correct except that. We never never plug in when doing limits.
    That is a completely wrong way to think about limits.

    What happens to as
    That is, h is 'close to' but not equal to zero. Unless that is clear to you then you will have trouble later on in mathematical proofs.
    You are absolutely correct, I actually knew that, I'm just so used to saying "plug it in", thanks a ton for the clarification.
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