Q:

How to find asymptotes of $y=ax+b+\frac{c+\sin x}{x}$

How can we find the asymptotes of $y=ax+b+\frac{c+\sin x}{x}$?

A:

HINT: Notice that when $|x|$ is very large, the fraction $$\frac{c+\sin x}x$$ is very small. (Why?) Thus, when $|x|$ is very large,
$$y=ax+b+\frac{c+\sin x}x\approx ax+b\;.$$

