The function $f_n(x) = n \sin(x/n)$. Then which option is the correct?
(a) does not converge for any $x$ as $n \to\infty$.
(b) converges to the constant function $1$ as $n \to\infty$.
(c) converges to the function $x$ as $n \to\infty$.
(d) does not converge for all $x$ as $n \to\infty$.
If $x=n\pi$ then function will be zero. But what should be the general case? Thanks for help.