$(4$ points$)$ Consider the two functions $f,g$:$R^{2}R$ defined by:

$f(x,y)$:$=\frac{x^{2}y}{y},g(x,y)$:$=\frac{x^2{y}^2-1}{y-1}$

a$)(2$ points$)$ By considering the value of $f(x,y)$ along the lines $x=0$ and $x=\sqrt[\phantom{2}]{y},$ show that the limit $\underset{(x,y)(0,0)}{lim}f(x,y)$ does not exist.

b$)(2$ points$)$ By considering the value of $g(x,y)$ along several different straight lines through $(1,1),$ show that the limit $\underset{(x,y)(1,1)}{lim}g(x,y)$ does not exist.