Toronto Math Forum

MAT334--2020S => MAT334--Tests and Quizzes => Quiz 2 => Topic started by: Yiheng Bian on January 30, 2020, 12:42:13 AM

Title: TUT5101 QUIZ2
Post 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
$$
\text{limit is zero}
$$

Title: Re: TUT5101 QUIZ2
Post by: Victor Ivrii on January 30, 2020, 06:39:52 AM
Wrong reasoning
Title: Re: TUT5101 QUIZ2
Post by: Yiheng Bian on January 30, 2020, 09:25:16 PM
Sorry sir, , could you point it out?
Title: Re: TUT5101 QUIZ2
Post by: Victor Ivrii on January 31, 2020, 09:05:11 AM
You cannot use LH out of the box for complex variables. You need to consider $z=re^{i\theta}$ and consider $\bigl|\dfrac{\operatorname{Log}(z)}{z}\bigr|$ ...
Title: Re: TUT5101 QUIZ2
Post by: Yiheng Bian on January 31, 2020, 11:31:11 PM
Ok, I got it. Thank you sir