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Math Help - Analysis

  1. #1
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    Analysis

    I just could not figure out how to get epsilon at the end.

    If f is continuous at a, and g is continuous at a, show that f+g is continuous at a.
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  2. #2
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    Quote Originally Posted by thahachaina View Post
    I just could not figure out how to get epsilon at the end.

    If f is continuous at a, and g is continuous at a, show that f+g is continuous at a.
    Hint: |f(x)+g(x)-f(a)-g(a)| = |[f(x)-f(a)]+[g(x)-g(a)]| \leq |f(x)-f(a)|+|g(x)-g(a)|
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  3. #3
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    Thanks buddy. But thats what i did. and both the terms you get at the end is less than epsilon. So when u add up, you get 2 epsilon. Don't i need to get "epsilon" as opposed to "2epsilon". My prof is picky about that.
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  4. #4
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    Quote Originally Posted by thahachaina View Post
    Thanks buddy. But thats what i did. and both the terms you get at the end is less than epsilon. So when u add up, you get 2 epsilon. Don't i need to get "epsilon" as opposed to "2epsilon". My prof is picky about that.
    Make both |f(x)-f(a)|,|g(x)-g(a)| smaller than \frac{\epsilon}{2}.
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