Problem $5\mathrm{.}1.$ Let $f_1$:$RR$ and $f_2$:$RRbe$ defined $by$

$f_1(x)=\{\begin{array}{cc}1,& x>0\\ [x,& x0]\text{a}\text{n}\text{d}& f_2(x)=x^2\end{array}$

$isf$:$R{R}^2$ defined $byf(x)=($:$f_1(x),f_2(x)$:$)$ continuous? Briefly explain.

Problem $5\mathrm{.}2.$ Let $F$:$R^2{R}^{2}be$ defined $by$

$F(x,y)=($:$e^{x}log(|y|+1),x{y}^2$:$)$

compute

$\underset{(\text{:}x,y\text{:})(\text{:}0,e-1\text{:})}{lim}F(x,y)$

briefly explain how you make your computation.