$($b$)$ Define the concept of continuity and explain it using an appropriate diagram.

$($c$)$ Show that the polynomial function $f(x,y)=2x^2-y(x+y)-(x^2-y^2)$ is continuous at the point $(2,4).$

and find $\frac{\text{d}\text{e}\text{l}\text{f}(x,y)}{\text{d}\text{e}\text{l}\text{x}}-=\underset{h0}{lim}\frac{f(x+h,y)-f(x,y)}{h}$ at the point $(1,4).$

$($d$)$ Using the same method, find $\frac{\text{d}\text{e}\text{l}\text{f}(x,y)}{\text{d}\text{e}\text{l}\text{y}}.$