prove by limit definition

f ,g are defined around x0 for which lim fg(x)=infinity when x->x0 .

prove that if k>0 so f>g>0 for every x on |x-x0|<k then

lim f(x)=infinity when x->x0 .


i tried:
for every n>0
every x in |x-x0|<k
makes fg>N
what now?

If g goes to infinity and f> g, then f goes to infinity. If neither f nor g goes to infinity, then fg does not.