Identifying Pole Order to the Test for Pole Procedure

[NJunJie]

Homework Statement

Test for pole procedure.
As attached powerpoint.
Pse advise.

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

Basically, what you have is right- although you should "suspect" that the pole at z= 7 is of order 3, not 7. I suspect that was a typo! A function, f(z) has "a pole of order n at z= z₀" if and only if (z- z₀)ⁿf(z) has a non-zero limit as z goes to z₀ and that is exactly what you have shown.