Question

`\lim_((x,y) \to \ (0,0)) (x^4 +y^3)/(x^4 + y^2)`

Answer 1

If
`x=0`, you have


`\displaystyle\lim_(y\to0)(y^3)/(y^2)=\lim_(y\to0)y=0`

But if
`y=0`, you have


`\displaystyle\lim_(x\to0)(x^4)/(x^4)=\lim_(x\to0)1=1`

So the limit does not exist.