Problem $4\mathrm{.}1.$ Let

$A=\{($:$x,y$:$)$:$10\}$

For the following function $f$:$A{R}^3$ what are the coordinate functions $off?$

$f(x,y)=($:$co{s}^2(x)+si{n}^2(y),\frac{x^2}{y},e^{x}log(y+1)$:$)$

Problem $4\mathrm{.}2.$ For the function $f$ from problem $4\mathrm{.}1,$ compute the following $limitsif$ possible, $ifitis$ not

possible, explain why.

$\underset{(\text{:}x,y\text{:})(\text{:}0,0\text{:})}{lim}f(x,y),\underset{(\text{:}x,y\text{:})(\text{:}0,\frac{}{2}\text{:})}{lim}f(x,y)$

Problem $4\mathrm{.}3.$ Let $f$:$R^{2}Rbe$ defined $byf(x,y)=xy-1.$ Write $an-proofto$ show that

$\underset{(\text{:}x,y\text{:})(\text{:}2,3\text{:})}{lim}f(x,y)=5$

Hint: $|xy-6|=|xy-2y+2y-6|$

Problem $4\mathrm{.}4.$ Let $f$:$R^{2}Rbe$ defined $byf(x,y)=x^2-y^2.$ Write $an-proofto$ show that

$\underset{(\text{:}x,y\text{:})(\text{:}2,3\text{:})}{lim}f(x,y)=-5$

Hint: $|x^2-y^2+5|=|x^2-4+9-y^2|.$