Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT334-2018F
»
MAT334--Tests
»
Quiz-2
»
Q2 TUT 0201
« previous
next »
Print
Pages: [
1
]
Author
Topic: Q2 TUT 0201 (Read 4543 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2607
Karma: 0
Q2 TUT 0201
«
on:
October 05, 2018, 06:12:58 PM »
Find all points of continuity of the given function:
\begin{equation*}
f(z)=\left\{\begin{aligned}
&\frac{z^4-1}{z-i}, &&z\ne i\\
&4i, &&z=i.
\end{aligned}
\right.
\end{equation*}
Logged
Xier Li
Newbie
Posts: 2
Karma: 2
Re: Q2 TUT 0201
«
Reply #1 on:
October 05, 2018, 08:27:59 PM »
$(z^4-1)/(z-i) = z^3+iz^2-z-i$ when $z\ne i$.
When $z\to i$, $z^4-1)/(z-i) \to -4i$.
This contradicts the fact that $f(z)=4i$ when $z=i$.
Thus, the function is continuous everywhere except $z=i.$
«
Last Edit: October 06, 2018, 05:40:33 AM by Victor Ivrii
»
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT334-2018F
»
MAT334--Tests
»
Quiz-2
»
Q2 TUT 0201