Question

For what values of x, if any, does `f(x) = 1/((x-5)sin(pi+(3pi)/x)` have vertical asymptotes?

Answer 1

`x=5 and x=+-3//n, n=+-1,+-2,+-3,...`,

Explanation:

`f(x)=1/(sin((3pi)/x)(5-x))`, using `sin (pi+a)=-sin a`

`f to oo`, as `x to` 3/(an integer) and 5#..