- #1
Bashyboy
- 1,421
- 5
The problem is to determine whether the function
##f(z) =
\left\{\begin{array}{l}
\frac{\overline{z}^2}{z}~~~if~~~z \ne 0 \\
0 ~~~if~~~z=0
\end{array}\right.##
is differentiable at the point ##z=0##. My two initial thoughts were to show that the function was not continuous at the point ##z=0##, which is may very well be (I don't know as of yet), or to show that the limit
##\frac{df}{dz} (z_0) = \lim\limits_{z \rightarrow z_0} \frac{f(z)-f(z_0)}{z-z_0}##
exists or does not. However, I am not sure of how to deal with the fact that ##f(z)## is a multi-part function.
Any suggestions?
##f(z) =
\left\{\begin{array}{l}
\frac{\overline{z}^2}{z}~~~if~~~z \ne 0 \\
0 ~~~if~~~z=0
\end{array}\right.##
is differentiable at the point ##z=0##. My two initial thoughts were to show that the function was not continuous at the point ##z=0##, which is may very well be (I don't know as of yet), or to show that the limit
##\frac{df}{dz} (z_0) = \lim\limits_{z \rightarrow z_0} \frac{f(z)-f(z_0)}{z-z_0}##
exists or does not. However, I am not sure of how to deal with the fact that ##f(z)## is a multi-part function.
Any suggestions?