Toronto Math Forum
MAT3342020S => MAT334Tests and Quizzes => Quiz 2 => Topic started by: Yiheng Bian on January 30, 2020, 12:42:13 AM

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
$$
\text{limit is zero}
$$

Wrong reasoning

Sorry sir, , could you point it out?

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

Ok, I got it. Thank you sir