What is the limit of $sin((x-1)/(2+x^2))$ as x approaches infinity?

Question

1358 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-11T21:54:17

$lim_(x->oo) sin ( (x-1)/(x^2+2) ) = 0$

We have that:

$lim_(x->oo) (x-1)/(x^2+2) = lim_(x->oo) (1-1/x)/(x+2/x) = 0$

As $sinx$ is continuous in $x=0$ :

$lim_(x->oo) sin ( (x-1)/(x^2+2) ) = sin (lim_(x->oo) (x-1)/(x^2+2) ) = sin (0) = 0$

What is the limit of sin((x-1)/(2+x^2))sin((x-1)/(2+x^2)) as x approaches infinity?