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Math Help - real anaylsis limit

  1. #1
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    real anaylsis limit

    Give examples of functions f and g such that f and g do not have limits a ta point c, but such that both f+g and fg have limits at c
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  2. #2
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    Take
    f(x)=1 for x<=c and f(x)=-1 for x>c,
    g(x)=1 for x>c and g(x)=-1 for x<=c.
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  3. #3
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    Quote Originally Posted by batman View Post
    Take
    f(x)=1 for x<=c and f(x)=-1 for x>c,
    g(x)=1 for x>c and g(x)=-1 for x<=c.
    I dont understand what you did. For one of the examples i get f(x)=1/x and g(x)=-1/x both of the limits DNE but the limit of f(x)+g(x)=0, just cant find an example for the product one. Any ideas??
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  4. #4
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    I took:
    -the function f that is 1 if x is less than or equal to c and is -1 if x is greater than c
    -the function g that is -1 if x is less than or equal to c and is 1 if x is greater than c

    Both functions don't have a limit at c (approaching c from the left gives a different value than approaching c from the right), also you have f+g = 0 and f*g= -1 so that both f+g and f*g have limits at c.
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