Please how can I show that the $lim_{n \rightarrow \infty}\int_{\Re^+}f_n d\mu$ covergers and determine its limit in the following cases of $f_n: \Re^+ \rightarrow \Re$ \\
a)$f_n(x) = sin(nx) \chi_{[0,n]}(x)$.b) $f_n(x)= \frac{ne^{-nx}}{\sqrt{1+n^{2}x^{2}}}$ c)$f_n(x)= \frac{ne^{-x}}{\sqrt{1+n^{2}x^{2}}}$.