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Math Help - Finding Limits

  1. #1
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    Finding Limits

    Hi I started limits today and I'm having trouble with two problems. Any help would be appreciated.

    The first problem is
    lim = -2x - 4 / x^3 + 2x^2
    x->-2

    The 2nd problem is
    lim = x^4 - 1 / x^3 - 1
    x->1

    Thanks guys. These two problems have been killing me for the last two hours. =(
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  2. #2
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    Quote Originally Posted by Afterme View Post
    The first problem is
    lim = -2x - 4 / x^3 + 2x^2
    x->-2
    Factor -2(x+2)/x^2(x+2) and cancel.

    The 2nd problem is
    lim = x^4 - 1 / x^3 - 1
    x->1
    Factor (x-1)(x^3+x^2+x+1)/(x-1)(x^2+x+1) and cancel.
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  3. #3
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    omg thanks. I can't believe I forgot something so simple . Thank you for helping me.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    remember, your goal here is to simplify the function so that you can possibly plug in the number x is tending to. if this is not possible, then we have to deal with things differently. however, in both these cases, it is possible
    Quote Originally Posted by Afterme View Post
    Hi I started limits today and I'm having trouble with two problems. Any help would be appreciated.

    The first problem is
    lim = -2x - 4 / x^3 + 2x^2
    x->-2
    hint: factorzie

    note that \frac {-2x - 4}{x^3 + 2x^2} = \frac {-2(x + 2)}{x^2(x + 2)}

    The 2nd problem is
    lim = x^4 - 1 / x^3 - 1
    x->1

    Thanks guys. These two problems have been killing me for the last two hours. =(
    hint: the numerator is the difference of two squares and the denominator is the difference of two cubes

    so, \frac {x^4 - 1}{x^3 - 1} = \frac {(x^2 - 1)(x^2 + 1)}{(x - 1)(x^2 + x + 1)} = \frac {(x + 1)(x - 1)(x^2 + 1)}{(x - 1)(x^2 + x + 1)}

    EDIT: argh! and i am late again
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