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## Homework Statement

Show that the following limit exists and find its value.

limit(x,y approaches 0,0) [ (y^3) / (|x| + y^2) ]

## The Attempt at a Solution

this was on a test and this is what i did. i got 4/12 pts on this.

i did the limit along the x-axis (y=0)

:

f(x,0) = (0^3) / ( |x| + 0 ) = 0

so the limit = 0 along x axis

along y axis (x=0):

f(0,y) = (y^3) / (0 + y^2) = y

and the limit (y goes to 0) y = 0

along x = y^2:

f(y^2,y) = (y^3) / (y^2 + y^2) = (y^2*(y)) / (y^2(1+1)) and y^2 cancels leaving y/2

and the limit y goes to 0 of y/2 = 0 along x=y^2

therefore limit(x,y approaches 0,0) [ (y^3) / (|x| + y^2) ]