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Math Help - arithmetic of sequences

  1. #1
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    arithmetic of sequences

    Let S (subset) R, and let f, g be functions from S to R. If f and g are continuous at
    a ia an element of set S, then prove that h(x) = f(x) + g(x) is also continuous at a.

    Hint: look at the proof of the arithmetic of sequences.
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  2. #2
    Senior Member vincisonfire's Avatar
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    A function is continuous at point a if
     \lim_{x\to{a}} f(x) = f(a) AND f(a) exist.
    If you already know that the two functions are continuous at a then
     \lim_{x\to{a}} h(x) = \lim_{x\to{a}} f(x)+g(x) = \lim_{x\to{a}} f(x) +\lim_{x\to{a}} g(x) = f(a) + g(a) = h(a)
    All this by definitions.
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