Question

What is the limit of `(x / cos (-3x))` as x approaches infinity?

Answer 1

the limit wiil alternate between `-oo` and `oo`

Explanation:

`lim_{x to oo} (x / cos(-3x))`

`=lim_{x to oo} (x / cos (3x))` as `cos psi = cos (- psi)`

`= 1/( cos (3x)) lim_{x to oo} x`

because cos (3 x) is bounded and periodic, ie `cos(-3 x) in [-1,1]` it can be taken out of the limit

but note that, as `x to oo`, the limit wiil alternate between `-oo` and `oo` as the cosine term changes sign with frequency `3/pi`