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**shadow_2145** Locate each of the isolated singularities of the given function and tell whether it is a removable singularity, a pole, or an essential singularity. If the singularity is removable, give the vlaue of the function at the point; if the singularity is a pole, give the order of the pole.

(1) $\displaystyle \frac{e^z-1}{z}$

Mr F says: Removable singularity at z = 0. (Expand e^z, simplify numerator and note that z is a common factor of numerator and denominator .....) Define f(0) = 1.

(2) $\displaystyle \frac{z^4-2z^2+1}{(z-1)^2}$

Mr F says: Removable singularity at z = 1. (Factorise the numerator .....) Define f(1) = 4.

(3) $\displaystyle \frac{2z+1}{z+2}$

Mr F says: Simple pole at z = -2 because (z + 2) f(z) is differentiable.

If anyone could show me how to do any of these, I would appreciate it. I don't understand it..Thanks!