Toronto Math Forum
MAT334--2020S => MAT334--Tests and Quizzes => Quiz 2 => Topic started by: Yiheng Bian on January 30, 2020, 12:42:13 AM
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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
$$
\text{limit is zero}
$$
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Wrong reasoning
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Sorry sir, , could you point it out?
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You cannot use LH out of the box for complex variables. You need to consider $z=re^{i\theta}$ and consider $\bigl|\dfrac{\operatorname{Log}(z)}{z}\bigr|$ ...
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Ok, I got it. Thank you sir