Question

For what values of x, if any, does `f(x) = 1/((x^2-4)cos(pi/2+(7pi)/x)` have vertical asymptotes?

Answer 1

`x = +-2, +-7( 1, 1/2, 1/3, 1/4, ...)`

Explanation:

The vertical asymptotes are given by

zero of `x^2-4=0` and `cos(pi/2+7/xpi)=0 => -sin(7pi/x)`.

These are

`x = +-2` and `7/k, k = +-1, +-2, +-3, ...`

Note that k = 0 sends `x to +-oo` to make kx read 7 .

The ad hoc graph is not to scale.
graph{-1/((x^2-4)sin(21.991/x) [-3.51, 3.47, -17, 17]}