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Math Help - one-sided limits

  1. #1
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    Talking one-sided limits

    lim x-->2- (-4x^3+1/x-2)

    find the limit as x approaches 2 from the left.

    Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by kristenstemmer View Post
    lim x-->2- (-4x^3+1/x-2)

    find the limit as x approaches 2 from the left.

    Thanks!
    Just making sure...is it \lim_{x\to2^-}\frac{-4x^3+1}{x-2}?
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  3. #3
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    Smile

    Yes, that is correct. Sorry, I don't know how to make it look like that
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Just making sure...is it \lim_{x\to2^-}\frac{-4x^3+1}{x-2}?
    Take note of the following:

    As we get closer to 2 from the left, -4x^3+1 gets closer and closer to -31, but x-2 approaches "negative" zero.
    This implies that the ratio \frac{-4x^3+1}{x-2} approaches +\infty.

    Thus, \lim_{x\to2^-}\frac{-4x^3+1}{x-2}=+\infty
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