Suppose $U \subset \C$ is a domain and $f \colon U \to \C$. Prove that if the following limit exists \begin{equation*} g(z) = \lim_{h \to 0} \frac{f(z+h)-f(z)}{\bar{h}} \end{equation*} for all $z \in U$ (note the bar on the $h$), then $f$ is real differentiable, and satisfies

Sketch the vector field vector f( vector r ) = 8vector r in the xy-plane. select all that apply. the length of each vector is 8. the lengths of the vectors decrease as you move away from the origin. all the vectors point away from the origin. all the vectors point in the same direction. all the vectors point towards the origin. the lengths of the vectors increase as you move away from the origin.