limit at infinity $f(x)=x+ax \sin(x)$ Let $f:\Bbb R\rightarrow \Bbb R$ be defined by $f(x)= x+ ax\sin x$.
I would like to show that if $|a| < 1$, then $\lim\limits_{x\rightarrow\pm \infty}f(x)=\pm \infty$.
Thanks for your time.

HINT: Rewrite the function as $f(x)=(1+a\sin x)x$. Now, what is $\inf_{x\in\Bbb R}(1+a\sin x)$? What does this tell you about the smallest possible value of $|f(x)|$ in terms of $x$?
