Problem $4\mathrm{.}7.$ Let $f$:$R^{2}Rbe$ defined $by$

$f(x,y)=\{\begin{array}{cc}0,& x=0=y\\ 2x^2\frac{y}{x^4+y^2},& \text{O}\text{t}\text{h}\text{e}\text{r}\text{w}\text{i}\text{s}\text{e}& \end{array}$

$(a)$ Let $x(t)=t$ and $y(t)=at$ for $a0(so$ this path $is$ a line through the origin $of$ slope

$a)$ Notice that $ast0,x(t),y(t)0.$ Compute $\underset{t0}{lim}f(x(t),y(t)).$

$(b)$ Let $x(t)=t$ and $y(t)=t^2.$ Notice that $ast0,x(t),y(t)0.$ Compute

$\underset{t0}{lim}f(x(t),y(t)).$

$(c)Isf$ continuous $at$ the point $($:$0,0$:$)?$