Pure Maths - limit

我覺得第二行和第三行都有問題
第二行是g(x)﹐第三行是f(x)/g(x)
∞*∞=∞ 所以 lim [f(x) g(x)] at x = a
= lim [f(x)] lim [g(x)] at x = a
= ∞*∞
= ∞
但 ∞/∞ 是無定義﹐所以要用洛必達法則。
螞蟻雄兵該答案中的 lim [g(x)] at x = 0 = lim [x] at x = 0 = 0 不是 ∞

I think there is a typo error in the question.
In the second line, f(x) should be g(x).

If lim of f(x) at x = a is infinity，and lim of f(x) at x = a is infinity,
is it true that lim of [f(x) g(x)] at x = a is infinity?
Sol
We can not sure ,so it is not true.
example
lim(x->0)_1/x^2 =inifite
lim(x->0)_[(1/x^2)*x^2]=1