Let the function (f: R^2⇢R) be (f(x, y) = \frac{xy^2}{ x^3+... | Mathematics for Economy | SolveeIt | Solveeit

Today, August 24

Question

Let the function $f: R^2⇢R$ be $f(x, y) = \frac{xy^2}{ x^3+ 2xy + y^3}\,\, f(0, 0) = 0.$ Then

A

f is differentiable at (0, 0).

B

f, does not exist at (0, 0).

C

does not exist at (0, 0).

D

f is not continuous at (0, 0).

Answer

f is not continuous at (0, 0).

Explanation

Solution

The correct option is (D): f is not continuous at (0, 0).