Suppose that a function $f(x)$ defined on $[0,1]$ satisfies $f(1/n)\to 0$ as $n\to\infty$. Is it true that $f(x)\to 0$ as $x\to 0^+$? and show that
(a) $f$ is continuous on $[0,1]$ ?
(b) $f$ is differentiable $(0,1)$ ?
I think this will be true case when $f(x)$=$sin(x)$ but I am a bit confused how to prove for any function and how to use $\epsilon$ _ $\delta$ to prove that. Please if any one can help me with this problem.