# real anaylsis limit

• Oct 21st 2008, 07:21 AM
bigb
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
• Oct 21st 2008, 08:14 AM
batman
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.
• Oct 21st 2008, 12:19 PM
bigb
Quote:

Originally Posted by batman
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??
• Oct 21st 2008, 12:49 PM
batman
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.