MAT334--2020S > Quiz 2

TUT5101 QUIZ2

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Yiheng Bian:
Question:
$$h(z)=\frac{Log(z)}{z}$$
We know when
$$z \rightarrow \infty$$
$$Log(z) \rightarrow \infty$$
So we can use L'Hopital rules and get
$$\frac{1}{z}$$
So
$$\text{limit is zero}$$

Victor Ivrii:
Wrong reasoning

Yiheng Bian:
Sorry sir, , could you point it out?

Victor Ivrii:
You cannot use LH out of the box for complex variables. You need to consider $z=re^{i\theta}$ and consider $\bigl|\dfrac{\operatorname{Log}(z)}{z}\bigr|$ ...

Yiheng Bian:
Ok, I got it. Thank you sir