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Math Help - Another question on Limits

  1. #1
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    Another question on Limits

    Given:

    \lim_{\Delta x \to 2}

    2-x
    ___________________
    x^2-4

    What would I do to solve down on this?
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  2. #2
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    Hello buddy.

    Quote Originally Posted by jimmyp View Post
    Given:

    \lim_{\Delta x \to 2}

    2-x
    ___________________
    x^2-4

    What would I do to solve down on this?
    Hint: (x-2)(x+2) = x^2-4

    = lim \frac{2-x}{(x-2)(x+2)}

    Note that 2-x = - (x-2)

    = lim \ -\frac{x-2}{(x-2)(x+2)} = - lim \frac{1}{x+2} = -1/4

    x to +2

    Cheers
    Rapha
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  3. #3
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    Sorry the lim Delta x -> 2 was suppose to read just lim x -> 2

    I don't believe your technique still holds in that case?
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  4. #4
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    Talking

    Quote Originally Posted by jimmyp View Post
    Sorry the lim Delta x -> 2 was suppose to read just lim x -> 2

    I don't believe your technique still holds in that case?
    Why would the factoring and cancellation not work...? What did you get, when you tried to use that method, that led you to this conclusion?
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  5. #5
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    Quote Originally Posted by jimmyp View Post
    Sorry the lim Delta x -> 2 was suppose to read just lim x -> 2

    I don't believe your technique still holds in that case?
    Actually, because there is no " \Delta x" in the function, Rapha did that already assuming that you mean \lim_{x\rightarrow 2} \frac{2- x}{x^2- 4}
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    Actually, because there is no " \Delta x" in the function, Rapha did that already assuming that you mean \lim_{x\rightarrow 2} \frac{2- x}{x^2- 4}
    Sorry - I now see where my logic was flawed. Thank you both.
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