I came across a problem which says:
Let $P$ be a polynomial of degree $k>0$ with a non-zero constant term.Let $f_n(x)=P(x/n), \, \forall x \in (0,\infty)$. Then which of the following is/are true?
(a) $\lim f_n(x)=\infty \quad \forall x \in (0,\infty)$
(b) $\exists x \in (0,\infty)$ such that $\lim f_n(x)>P(0)$
(c) $\lim f_n(x)=0 \quad \forall x \in (0,\infty)$
(d) $\lim f_n(x)=P(0) \quad \forall x \in (0,\infty)$
I do not know how to approach the problem. Any kind of hints will be helpful. Thanks in advance for your time.