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Math Help - Ap Calc question.

  1. #1
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    Ap Calc question.

    Hey, need help with some calculus stuff.

    if f(x) = (sqrt(2x+5)-sqrt(x+7)) / (x-2) for x ≠ 2, and if f is continuous at x = 2, then k = ?
    f(2) = k

    Sorry, I don't know how to do the symbols, so I had to type it out like this. sqrt = square root.

    I also need to know how you do it, not just the answer.

    Thanks in advance for the help. I really appreciate it.
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  2. #2
    A Plied Mathematician
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    The crux of the matter is this: what is the "calculus definition" of continuity at a point?
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  3. #3
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    Um, I don't know. You're going to have to walk me through this one. I'm an idiot when it comes to Calculus. Every other math is easy for me. But Calculus is just something else.
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  4. #4
    A Plied Mathematician
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    The calculus definition of continuity at a point (which is entirely equivalent to the epsilon-delta definition) goes like this: function f(x) is continuous at a if and only if

    \displaystyle\lim_{x\to a}f(x)=f(a).

    This statement means three things:

    1. The limit \displaystyle\lim_{x\to a}f(x) exists.
    2. The function f(x) is defined at a; that is, f(a) exists.
    3. The limit is equal to the function's value at a.

    Any one of those could fail, leaving you with a discontinuous function at a.

    So, does this give you any ideas?
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