Toronto Math Forum
MAT3342020F => MAT334Tests and Quizzes => Quiz 5 => Topic started by: Xun Zheng on November 06, 2020, 11:13:23 AM

Locate each of the isolated singularities of the given function and tell whether it is a removable singularity, a pole, or an essential singularity (case (3)). If the singularity is removable, give the value of the function at the point; if the singularity is a pole, give the order of the pole.
$$\frac{e^z1}{z}$$
Here is my answer:
 First, we get that z=0 is a singularity.
 Next, we have $$\lim_{z\to 0}\frac{e^z1}{z}=\lim_{z\to 0}\frac{e^z}{1} = \lim_{z\to 0}{e^z} = 1$$
 Hence, by definition, it is a removable singularity.