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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- October 21st 2008, 07:21 AMbigbreal 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

- October 21st 2008, 08:14 AMbatman
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. - October 21st 2008, 12:19 PMbigb
- October 21st 2008, 12:49 PMbatman
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.