Question

For what values of x, if any, does `f(x) = 1/((x-4)sinx)` have vertical asymptotes?

Answer 1

`x=4 or x=kpi, k in ZZ`

Explanation:

Vertical asymptotes occur at points where the denominator is zero since division by zero is undefined.

This is hence when `(x-4)=0 or sinx=0`

ie, when `x=4 or x=0+kpi, kinZZ`