hello you all, i'm new here.. i'd like if you help me in this question.

f and g are function defined in apunctured neighborhood of X, and L is a real number._{0}

assuming lim(x->x_{0}) (f times g)(x)=L

i need to prove\disprove that if lim(x->x_{0}) f(x)=infinity, then lim(x->x_{0}) g(x) exists.

it would be very helpful if you also instruct me in the general way of proving such questions, because i'm kinda new in this subject...

thx!