- #1

Phyrrus

- 21

- 0

## Homework Statement

lim (x,y) -> (0,0) (4x^3*y^4)/(3y^4+5x^8)

When y=kx -> lim x->0 = 0

The limit definitely is zero, but I can't prove it.

## The Attempt at a Solution

? < lim (x,y) -> (0,0) (4x^3*y^4)/(3y^4+5x^8) < lim (x,y) -> (0,0) (4|x^3|*y^4+(15/4)|x^3|x^8)/(3y^4+5x^8) = (3/4)|x^3|

How do you find the lower limit of such a proof?

Can it be said that lim (x,y) -> (0,0) (4x^3*y^4)/(3y^4+5x^8) is equal to lim (x,y) -> (0,0) (|4x^3|*y^4)/(3y^4+5x^8) and therefore find the 'sandwich' of the new function?