Answer and Step-by-step explanation:
a.)x^2 and y^2 are always greater than zero.(assuming real x and y).
=>x^2<=x^2+y^2
=>|x|(x^2)<=|x|(x^2+y^2)
=>|x^3|<=|x|(x^2+y^2)
b. similarly, |y^3|<=|y|(x^2+y^2)
=>|f(x,y)|=|x^3+y^3|/(x^2+y^2)=|x|+|y|
c. let h is very small number (close to zero but positive)
lim (x,y)-> (0,0) f(x,y)=(x^3+y^3)/(x^2+y^2)
putting x=h and y=h and approaching h->0
lim h->0 f(h)=2h=0
There is another explanation attached below
