False. Use the example the book gives.

The function f(x,y) is defined on an open disk containing (0,0). Which means f is continous if and only if,

lim [(x,y)-->(0,0)] f(x,y) = f(0,0)=0

But if you choose the path x=y both approaching zero the limit of f(x,y) is then 1! It must always be zero if it continous.

This is Mine 55th Post!!!