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Math Help - Limit question.

  1. #1
    Member integral's Avatar
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    Limit question.

    I'm going back over my calculus book now that the year is over, doing all the questions to make sure that I know the subject. I worked this limit problem and got it wrong but I don't know how to solve it correctly (without L'Hospital's).
    \lim_{x \to 7} \frac{\sqrt{x+2}-3}{x-7}

    I said DNE, but the answer is 1/6. Anyone know how to solve? thx.
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  2. #2
    A Plied Mathematician
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    Try thinking of the denominator as the "difference of squares" and factoring it.
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  3. #3
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    Quote Originally Posted by integral View Post
    I'm going back over my calculus book now that the year is over, doing all the questions to make sure that I know the subject. I worked this limit problem and got it wrong but I don't know how to solve it correctly (without L'Hospital's).
    \lim_{x \to 7} \frac{\sqrt{x+2}-3}{x-7}

    I said DNE, but the answer is 1/6. Anyone know how to solve? thx.
    Dear integral,

    Multiply both the numerator and the denominator by \sqrt{x+2}+3.
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  4. #4
    Member integral's Avatar
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    I got it. Thanks
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