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Math Help - Division of a real analytic function

  1. #1
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    Division of a real analytic function

    Can anybody can help me?

    On some interval [a,b] suppose that I have a real analytic function f and a real contiuous function g, where g is different from zero in [a,b]. Does f/g will be real analytic on [a,b]? Otherwise what can I say on the function f/g ?
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  2. #2
    Behold, the power of SARDINES!
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    What if g(x) is the piecewise linear function that takes values

    \displaystyle g(a)=1, g\left( \frac{a+b}{2}\right)=2,g(b)=1

    is the function

    \displaystyle h(x)=\frac{f(x)}{g(x)} analytic?
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