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Math Help - How to calculate the following limit

  1. #1
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    How to calculate the following limit

    Can someone please explain to me the steps to get the limit of the following?

    \frac{x^4-1}{x-1}

    As x \rightarrow 1

    Thanks.
    Last edited by softwareguy; March 26th 2010 at 09:17 PM.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by softwareguy View Post
    Can someone please explain to me the steps to get the limit of the following?

    x^4-1/x-1

    As X --> 1

    Thanks.
    \frac{x^{4}-1}{x-1}=\frac{(x^{2}+1)(x^{2}-1)}{x-1}=\frac{(x^{2}+1)(x+1)(x-1)}{x-1}=(x^{2}+1)(x+1)

    Now calculate the limit as x goes to 1
    Last edited by harish21; March 22nd 2010 at 08:23 PM.
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  3. #3
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    Somehow the answer is 4. How did they get the answer 4? I don't see it...
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  4. #4
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by softwareguy View Post
    Somehow the answer is 4. How did they get the answer 4? I don't see it...
    Did you even try this?

    You are left with (x^{2}+1)(x+1)

    As x goes to 1 (X--->1), the limit becomes:

    (1^{2}+1)(1+1) = (2)(2)

    What do you get when you multiply 2 and 2?
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  5. #5
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    Ouch, sorry about that! I totally spaced. Thanks very much for your help!
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