[Multivariable Calculus 5] Solid angles and line integrals

1. Solid angles and the sun and moon

5. Continuity of functions

Which of the following functions are continuous at $(0,0)$? \begin{align*} f_1(x,y) &= \begin{cases} \frac{(x+y)^2}{x^2 + y^2} & (x,y) \neq (0,0), \\ 0 & (x,y) = (0,0) \end{cases} \\ f_2(x,y) &= \begin{cases} \frac{x^3 + y^3}{x^2 + y^2} & (x,y) \neq (0,0), \\ 0 & (x,y) = (0,0) \end{cases} \\ f_3(x,y) &= \begin{cases} \frac{xy}{x^2 + y^2} & (x,y) \neq (0,0), \\ 0 & (x,y) = (0,0) \end{cases}. \\ \end{align*}

Spoiler