Find the linear equation which approximates the function $f(x,y)=e^{x}cosy$ at the point $(0,,-1).$

Show that the limit $\underset{(x,y)(0,0)}{lim}\frac{x{y}^2}{x^2+y^4}$ does not exist.

Identify the largest set on which the function $f(x,y,z)=\frac{xyz}{x-y^2+z^2}$ is continuous.