(Solved): 5. If f(x0,y0)=3, what can you say about: lim(x,y)(x0,y0)f(x,y) if f is continuou ...

5. If $f\left(x_0,y_0\right)=3$, what can you say about: ${\lim }_{(x,y)?\left(x_0,y_0\right)}f(x,y)$ if $f$ is continuous at $\left(x_0,y_0\right)$ ? If $f$ is not continuous at $\left(x_0,y_0\right)$ ? Give reasons for your answers. 6. The function $f(x,y)=xy\frac{x^2}{x^2+y^2}$ ishot defined at $(x,y)=(0,0)$. Sketch the graph of the function using a 3D graphing utility and determine what $f(0,0)$ should be in order to continuously extend the function to the origin.