What are the asymptote(s) and hole(s), if any, of # f(x) =sin(pix)/x#?
First you have to calculate the zero marks of the denominator which in this case is
As you see we have a common zero mark. This means that it's not an asymptote but a hole (with
Now we take the
but because there is only one kind of exponent of
Now, if the exponent is bigger in the numerator than of the denominator that means that there's a diagonal or a curved asymptote. Otherwise, there's a straight line. In this case, it's going to be a straight line. Now you divide the a values of the numerator by the a value of the denominator.