- #1

Jamin2112

- 986

- 12

## Homework Statement

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

## Homework Equations

So it says,

**Definition:**A function f(x,y) is

*continuous*at 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) is

*discontinuous*at 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.

## 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?

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