Question

What is the limit of `cosx/(x^2-sinx)` as x approaches infinity?

Answer 1

0

Explanation:

`lim_{x to oo} cosx/(x^2-sinx)`

`cos x, sin x in [-1,1]` and are continuous for `x in [0, oo)`

the dominant term is the `x^2` term in the denominator

so `lim_{x to oo} cosx/(x^2-sinx) = 0`