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!