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Math Help - Limit of ln(x+1) as x->infinity

  1. #1
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    Limit of ln(x+1) as x->infinity

    Hi, I'm a bit rusty on my math since it is summer...
    but i have to do this summer assignment.

    The original question is which of the following functions has a horizontal asymptote at y=-1? and it lists like 5 equations, one which is y=ln(x+1)

    I'm thinking that you have to find the limit as x->infinity and negative infinity, and if the answer is -1, that is my equation. If that's wrong, point it out please.

    And no graphing calculator, and i really don't want to hand draw these graphs (i have to show work)

    Thanks!
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  2. #2
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    Quote Originally Posted by JOhkonut View Post
    Hi, I'm a bit rusty on my math since it is summer...
    but i have to do this summer assignment.

    The original question is which of the following functions has a horizontal asymptote at y=-1? and it lists like 5 equations, one which is y=ln(x+1)

    I'm thinking that you have to find the limit as x->infinity and negative infinity, and if the answer is -1, that is my equation. If that's wrong, point it out please.

    And no graphing calculator, and i really don't want to hand draw these graphs (i have to show work)

    Thanks!
    \lim_{x \to \infty} \ln(x+1) = \infty

    and \ln(x+1) is undefined in the reals for x\le -1

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by JOhkonut View Post
    Hi, I'm a bit rusty on my math since it is summer...
    but i have to do this summer assignment.

    The original question is which of the following functions has a horizontal asymptote at y=-1? and it lists like 5 equations, one which is y=ln(x+1)

    I'm thinking that you have to find the limit as x->infinity and negative infinity, and if the answer is -1, that is my equation. If that's wrong, point it out please.

    And no graphing calculator, and i really don't want to hand draw these graphs (i have to show work)

    Thanks!
    You don't need a calculator, there are many options if you have access to a computer. There should be a built in calculator with the operating system, or (not many people know this) just type the calculation into Google and Google calculator will give the answer. Not to mention the myriad of online function/graph plotters that you will find if you google for online graph plotter, the first hit is here.

    RonL
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  4. #4
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    Quote Originally Posted by CaptainBlack View Post
    You don't need a calculator, there are many options if you have access to a computer. There should be a built in calculator with the operating system, or (not many people know this) just type the calculation into Google and Google calculator will give the answer. Not to mention the myriad of online function/graph plotters that you will find if you google for online graph plotter, the first hit is here.

    RonL
    Actually, it's not that I don't have a graphing calculator, I'm just not allowed to use one for that problem. Do you think that just writing that the limit goes to infinity is sufficient?
    Last edited by CaptainBlack; August 14th 2008 at 11:14 AM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by JOhkonut View Post
    Actually, it's not that I don't have a graphing calculator, I'm just not allowed to use one for that problem. Do you think that just writing that the limit goes to infinity is sufficient?
    It depends on what you are supposed to know. If you know that \ln(x) increases without bound as x goes to infinity you need just say so.
    RonL
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  6. #6
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    Quote Originally Posted by CaptainBlack View Post
    It depends on what you are supposed to know. If you know that \ln(x) increases without bound as x goes to infinity you need just say so.
    RonL
    If it's mathematical common sense, then yes, i think I'm supposed to know that.
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  7. #7
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    Quote Originally Posted by JOhkonut View Post
    Actually, it's not that I don't have a graphing calculator, I'm just not allowed to use one for that problem. Do you think that just writing that the limit goes to infinity is sufficient?
    This depends on your teacher, but I would assume that it is efficient enough. One thing you can is rewrite the limit equation to prove your point even further.

    \lim_{x \rightarrow \infty} ln(x)

     \lim_{e^x \rightarrow \infty} e^{ln(x)}

    In order for a^x to go to infinity, the base must be positive and x must have a limit of infinity. Both of those work for this limit, so the following can be said:

    \lim_{x \rightarrow \infty} x
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