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Math Help - Limit Problem

  1. #1
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    Limit Problem

    (sqrt7-x)/(49-x^4) as x approaches sqrt7

    I multiplied by the conjugate to rationalize the numerator. I also factored the bottom... and I came up with this.

    (7-x)/(x^2+7)(x^2-7)

    What to do after this?
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  2. #2
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    \lim_{x \to \sqrt{7}} \frac{\sqrt{7} - x}{49-x^4}

    = \lim_{x \to \sqrt{7}} \frac{\sqrt{7} - x}{{\color{red}(7-x^2)}(7+x^2)}

    Try applying the difference of squares formula to the red
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  3. #3
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    haha so obvious... sometimes I don't see these things. Thank you sir!
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    Quote Originally Posted by Sturm88
    Hey I have a really silly question, but what is a root + a root. like sqrt7 + sqrt 7 in the problem I just posted...
    a + a = 2a. This is obvious right?

    Imagine a = \sqrt{7}
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  5. #5
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    So the answer is 28sqrt7?
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  7. #7
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    (1/64)-(1/x^2)/(x-8) as x approaches 8

    I used difference of squares on the top and I got this

    (1/8x+x)(1/8-x)/(x-8) stuck here.
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