Question Number 114790 by manuel2456 last updated on 21/Sep/20

lim_((x,y)→(0,0))  ((x^(3/2) y)/(x^3 +y^2 ))=?

Answered by Olaf last updated on 26/Sep/20

f(x,y) = ((x^(3/2) y)/(x^3 +y^2 ))  f(x,y) = (1/y).(x^(3/2) /(1+(x^3 /y^2 )))  Series expansion at x = 0 :  f(x,y) = (x^(3/2) /y)(1−(x^3 /y^2 ))+o(x^(11/2) )  f(x,y) = (x^(3/2) /y)−(x^(9/2) /y^3 )+o(x^(11/2) )  Assuming y = 0 :    lim_(x→0) f(x,y) = 0