Posted by T.Gracken on May 13, 2001 at 11:48:39:
In Reply to: Limits...please help!! *due monday* posted by scarletstarlett on May 12, 2001 at 23:16:14:
: Find two functions f and g such that lim (as x approaches 0) of f(x) and the lim (as x approaches 0) of g(x) does not exist but lim (as x approaches 0) of [f(x)+g(x)] does exist.
: Could someone explain how to do this? I don't even understand how this would work or why! Thanks
I won't explain it, but if you use your imagination...
you might let f(x)=1/[sin(x)]; then the limit (as x approaches 0) of f(x) d.n.e.
and let g(x)=-cot(x); then the limit (as x approaches 0) of g(x) d.n.e.
But f(x)+g(x)= [1-cos(x)]/[sin(x)] and by Hospitals rule: the limit (as x approaches 0) of [f(x)+g(x)] = the limit (as x approaches 0) of [sin(x)]/[cos(x)] = 0.