Real valued functions of several variables

$3.$ Determine whether the following functions have a limit as $(x,y)(0,0).$

$($a$)\frac{xy}{x^2+y^2}$

$($b$)\frac{x^{2}y}{x^2+y^2}$

$($c$)\frac{x^{2}y}{x^4+y^2}$

UCSB MATH $6$A

Week $4,$ Winter $2025$

$($d$)\frac{x^{2}y}{x^2+y^4}$