Problem $4\mathrm{.}5.$ Let $A=\{($:$x,y$:$)$:$($:$0,0$:$)($:$x,y$:$)\}.$

$(a)$ Let $f$:$ARbe$ defined $byf(x,y)=sin\frac{x}{y}.$ Show that $\underset{(\text{:}x,y\text{:})(\text{:}0,0\text{:})}{lim}f(x,y)$ does

not exist.

$(b)$ Let $f$:$ARbe$ defined $byf(x,y)=2\frac{x^2}{y}.$ Show that $\underset{(\text{:}x,y\text{:})(\text{:}0,0\text{:})}{lim}f(x,y)$ does

not exist.

Problem $4\mathrm{.}6.$ Let $B=\{($:$x,y,z$:$)$:$(x-1{)}^2+y+z^{3}0\}$ and

$f(x,y,z)=\frac{y+z^4+(x-1{)}^3}{y+z^3+(x-1{)}^2}$

Show that $\underset{(\text{:}x,y,z\text{:})(\text{:}1,0,0\text{:})}{lim}f(x,y,z)$ does not exist.