What is the Limit of f(x) as x Approaches Infinity?

[Fairy111]

Homework Statement

For the following function decide whether f(x) tends to a limit as x tends to infinity. When the limit exists find it.

Homework Equations

f(x)=[xsinx] / [x^2 +1]

The Attempt at a Solution

Im not really sure what method to use for this question.

 

[The Dagda]

well sinx cycles from -1 to 1, to infinity and x tends to infinity. What happens to:

$$x^2+1\;\lim_{x\rightarrow\infty}$$

 

[Fairy111]

x^2 + 1 tends to infinity as x tends to infinity. So infinity over infinity?

 

[The Dagda]

Actually not exactly as sinx goes from -1 to 1 to the limit of infinity and x goes to infinity so it's between - 1 x infinity and 1 x infinity, infinitely as x approaches infinity. Hehe that makes sense.

 

[psykatic]

As to my methodology,

$$\lim_{x\rightarrow\infty}\frac{xsinx}{x^2+1}$$

Taking $$x^2$$ common, we have the above equation as,
$$\lim_{x\rightarrow\infty}\frac{x^2(\frac{sinx}{x})}{x^2(1+\frac{1}{x^2})}$$

Now, cancelling $$x^2$$ terms and also we know that $$\frac{1}{\infty}=~0$$,

Thus, the function tends to?
(It can't get easier than this.. c'mon..)