Question 3For real numbers $a,b$, define $x_0,x_1,x_2,\ldots$ by $x_0=a$, $x_{n+1}=x_n+b\sin x_n$. If $b=1$, prove that the sequence converges to a finite limit for every $a$. If $b\gt 2$, prove that it diverges for some $a$.