Cal help

[junhoma]

The function f(x,y) = xy^2/(x^2+y^2) for ( x, Y) not equal to ( 0, 0) and 0 for (x Y) = ( 0, 0)

Discuss the domain of f and support your claims.

2. Find lim ( x,y) approaches (0, 0) f(x, y) and discuss the continuity of f(x, y)

please help me for this problem.

 

[tkhunny]

Is (0,0) in the Domain? You'll have to decide that, first.

 

[tkhunny]

The real conceptual leap, here, is that you must demonstrate limiting behavior on an entire disk. One must be able to approach from ANY direction. It is somewhat customary to hold each of x and y constant, respectively, and treat the remaining limit as a univariate problem. See if the function approaches the same value form both sides. This is part of a complete solution.

First, however, you MUST decide if (0,0) is in the Domain. You should draw on all you have learned before to answer this important question.