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**Quiz-6 / Re: Q6 TUT 0102**

« **on:**November 17, 2018, 04:44:07 PM »

my solution would be showed in the scan photos.

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my solution would be showed in the scan photos.

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I think I know how to prove essential part, by the definition provided by textbook. A singularity point is essential when it is neither equal to infinity or bounded. Hence, it is equivalent to say that limit does not exist at that singularity point because left side limit and right side limit are different. But for analytic part, I try to solve it by Riemann Cauchy equation, but the function itself is very complicated by separating u and z to a+bi and x+yi.

Hence, I wonder if we can have a better way to prove analytic part or I just need to keep calculating.

Hence, I wonder if we can have a better way to prove analytic part or I just need to keep calculating.

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I think some functions are common, whose derivatives are calculated in the previous courses(including high school courses). For example, I think Sinx is an example, x^m is another example. In the practice and test, if question doesn't ask you to use definition, I guess it is not necessary to use that. Meanwhile, the definition method can ensure you to get the correct answer, but it takes some time right?

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