improper integrals for negative functions(limit comparison test)

Question

The L.C.T(limit comparison test) for the improper integral is Surely,

$f>0$ and $g>0$ on the one interval, $I$ s.t. $a \in I$ (the $a$ implies the case $\pm\infty$)

$lim_{{x} \to {a}} {g \over f} = l >0 $

Then convergence or divergence of the $\int_I f dx$ and $\int_I g dx$ are same.

But What if the $f<0$ and $g<0$ for the limit value at $a$ , $l >0$ on the interval, $I$? Does limit comparison test still hold?

Thanks.

Answer 1

Hint: $\int_I f$ converges if and only if $\int_I(-f)$ converges and $(-f)/(-g) = f/g$.