$(10$ points$)$ Let $k>0,m>0be$ constants and let

$f(x,y)=\frac{x^{n-1}{y}^{2k}}{(2sinx{)}^{2m}+y^{2k}}$

where $nis$ a real number.

$(a)$ For what range $of$ values $n$ does $\underset{(x,y)(0,0)}{lim}f(x,y)$ not exist? Justify this using

techniques learned $in$ class.

$(b)$ For what range $of$ values $n$ does $\underset{(x,y)(0,0)}{lim}f(x,y)$ exist? What $i\frac{s}{a}re$ the $limi\frac{t}{s}?$

Justify this using techniques learned $in$ class.