# Math Help - Real Analysis Problem

1. ## Real Analysis Problem

Let f: (0,1] -> R be differentiable on (0,1], with |f(x)|<=1 for all x in (0,1]. For each n in N, let a(sub n)=f(1/n). Show that a(sub n), with n in N, converges.

2. Originally Posted by dhhnerd
Let f: (0,1] -> R be differentiable on (0,1], with |f(x)|<=1 for all x in (0,1]. For each n in N, let a(sub n)=f(1/n). Show that a(sub n), with n in N, converges.
Let $f(x) = \sin \tfrac{1}{x}$ then $f$ is differenciable on $(0,\infty)$ and $|f|\leq 1$. The sequence is $a_n = f(\tfrac{1}{n}) = \sin (n)$.
However, $\{a_n\}$ is not a convergent sequence.