When examining the behavior of f(x,y) = 5x² + 2.25x²y² as (x,y) approaches (0,0) and changing to polar coordinates, we find:
A) The function approaches 0, indicating that the limit exists and the function is continuous at (0,0) .
B) The function approaches infinity, indicating that the limit does not exist because the function's value increases without bound.
C) The function's behavior depends on the path taken to approach (0,0) , indicating that the limit does not exist.
D) The expression simplifies to a function of r only, making it easier to determine the limit as r approaches 0.
