(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I don't need to state the whole problem; it's the definitions at the beginning that are giving me trouble.

2. Relevant equations

So it says,

Definition:A function f(x,y) iscontinuousat a point (x_{0},y_{0}) if f(x,y) is defined at (x_{0},y_{0}), and if lim_{(x,y)-->(x0,y0) }f(x,y)=f(x_{0},y_{0}).

Definition:A function f(x,y) isdiscontinuousat a point (x_{0},y_{0}) if it is defined at (x_{0},y_{0}), and if either f(x,y) had no limiting value at (x_{0},y_{0}), or if lim_{(x,y)-->(x0,y0)}f(x,y) has no value.

The problem then gives me a function f(x,y)=(xy^{2}-y^{3})/(x^{2}+y^{2}) and asks whether lim_{(x,y)-->(0,0)}f(x,y) has a value.

3. The attempt at a solution

Something seems wrong about the definitions. Both of them say that f is defined at (x_{0},y_{0}). But what if f isn't defined there? In the function that I'm given, plugging in 0 for x and 0 for y means diving by zero. Type-o?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Advanced Multivariable Calculus / Continuity / Type-o?

**Physics Forums | Science Articles, Homework Help, Discussion**