Does y*ln(y^2+x^2) Approach Zero as (x, y) Goes to (0,0)?

[AHMAD MS]

Homework Statement

(x,y)-->(0,0) y*ln (y²+x²)

Homework Equations

!

The Attempt at a Solution

i've tried polar coordinates i end up with sinθ in it don't know how to proceed

and I've taken several paths like y=0 , x=0 , x=y² , x=y , x=y³
they all yeild zero

Edit : is it right if i after making polar sub. to say that :

r*sinθ * ln r² \leq r*ln r²
because if its right then problem solved :P

 

[LCKurtz]

Homework Statement

(x,y)-->(0,0) y*ln (y²+x²)

Homework Equations

!

The Attempt at a Solution

i've tried polar coordinates i end up with sinθ in it don't know how to proceed

and I've taken several paths like y=0 , x=0 , x=y² , x=y , x=y³
they all yeild zero

Edit : is it right if i after making polar sub. to say that :

r*sinθ * ln r² \leq r*ln r²
because if its right then problem solved :P

Almost. You need absolute values:

|r*sinθ * ln r²| \leq r*|ln (r²)|