Question: Find each limit.

(a) \(\underset{\Delta x\to 0}{\mathop{\lim }}\,\frac{f\left( x+\Delta x,y \right)-f\left( x,y \right)}{\Delta x}\)

(b) \(\underset{\Delta y\to 0}{\mathop{\lim }}\,\frac{f\left( x,y+\Delta y \right)-f\left( x,y \right)}{\Delta y}\)

for \(f\left( x,y \right)={{x}^{2}}+{{y}^{2}}\)