Let $(x_n)$ and $(y_n)$ be sequences of positive numbers such that $\lim \frac{x_n}{y_n} = 0$.
a) Show that if $\lim x_n = \infty$, then $\lim y_n = \infty$.
b) Show that if $y_n$ is bounded, then $\lim x_n = 0$.
For a, could I say, there exists a $N$ such that $\frac{x_n}{y_n} < 1$ for $n > N$. So $y_n > x_n$ for any $n > N$?
So, $\lim y_n = \infty$.