The easiest way of obtaining this would be for the one-sided limits to be different for both functions:
Then:
But,
Therefore does not converge at and neither does in the same way.
The sign function sgn(x) is defined as follows:
sgn(x)={x/lxl if x does not equal 0; 0 if x=0}
Use the sign function to define two functions f and g whose limits as
x -> 0 does not exist, but such that
(a) lim [f(x)+g(x)] does exist
x->0
(b) lim (f(x))(g(x)) does exist
x->0
Please show work too, itll be very helpful!