# Limit of multi variable func.

## Homework Statement

(x,y)-->(0,0) y*ln (y2+x2)

!

## 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

Last edited:

LCKurtz
Homework Helper
Gold Member

## Homework Statement

(x,y)-->(0,0) y*ln (y2+x2)

!

## 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)|