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Math Help - Determining infinite limits

  1. #1
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    Determining infinite limits

    2x^2(x-1)/(x+1)^3

    limit as x approaches  -1+ (right hand)

    I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello,
    Quote Originally Posted by NotEinstein View Post
    2x^2(x-1)/(x+1)^3

    limit as x approaches  -1+ (right hand)

    I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.

    \lim_{x\to-1^+}2x^2(x-1) = ? and \lim_{x\to-1^+}(x+1)^3 = ?

    hence what is the limit of the ratio \frac{2x^2(x-1)}{(x+1)^3} when x tends to -1^+ ?
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  3. #3
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    Quote Originally Posted by NotEinstein View Post
    2x^2(x-1)/(x+1)^3

    limit as x approaches  -1+ (right hand)

    I know the limit approaches negative infinity, but am having a hard time proving my answer by manipulating this function. Thanks in advance.
    The top tends to -4, the bottom tends to 0. As a denominator gets very small, the number itself gets very large. So the limit is infinity.
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  4. #4
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    Some editing (in red):

    Quote Originally Posted by Prove It View Post
    The top tends to -4, the bottom tends to 0{\color{red}^{+}}. As a denominator gets very small and positive, the number itself gets very large and negative (since the top is negative). So the limit is negative infinity.
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