Assume real value functions u, v of two variables have continuous partial derivatives at \(( x _ { 0 } , y _ { 0 } )\) . Show that \(f = u + i v\) has derivative \(f ^ { \prime } ( z _ { 0 } )\) at \(z _ { 0 } = x _ { 0 } + i y _ { 0 }\) if and only if
\[ \operatorname * { l i m } _ { r 0 } \frac { 1 } { \pi r ^ { 2 } } \int _ { | z - z _ { 0 } | = r } f ( z ) d z = 0 \ . \]