Question $1(10$ points$)$

Consider the function f$($x$,$y$)=\{(($sin$($x$^(2)+$y$^(2)))/($x$^(2)+$y$^(2)),($x$,$y$)!=(0,0)),(3,($x$,$y$)=(0,0))$:$\}$

a$.$ Determine $\backslash$lim$\_(($x$,$y$)->(0,$y$))$f$($x$,$y$)($Hint: Convert to polar coordinates$)$

b$.$ Explain why is f$($x$,$y$)$ not continuous at $(0,0)$ and modify the given multivariate

function so that it is continuous over the entire xy$-$plane.