What is the limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) ?

The limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) is diverges

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limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2)

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

diverges

Solution steps

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

Find two different paths to approach the point that gives different values for the limit

Limit of

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

along

x = 0 : 0

Limit of

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

along

x = y : \frac{1}{4}

= diverges

What is the limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) ?
The limit as (x,y) approaches (0,0) of (xycos(y))/(3x^2+y^2) is diverges