$In$ this problem $we$ show that the function

$f(x,y)=\frac{5x^2-y^2}{x^2+y^2}$

does not have a $limitas(x,y)(0,0).$

$(a)$ Suppose that $we$ consider $(x,y)(0,0)$ along the curve $y=4x.$ Find the $limit$

$in$ this case:

$\underset{(x,4x)(0,0)}{lim}\frac{5x^2-y^2}{x^2+y^2}=-\frac{11}{17}$

$(b)$ Now consider $(x,y)(0,0)$ along the curve $y=5x.$ Find the $limitin$ this

case:

$\underset{(x,5x)(0,0)}{lim}\frac{5x^2-y^2}{x^2+y^2}=-\frac{10}{13}$