- #1

makavelian

- 3

- 0

## Homework Statement

let f(x,y)=(x

^{4}+y

^{4})

^{1/3}

a)find f

_{1}for (x,y)[tex]\neq[/tex](0,0)

b)prove that lim(x,y)[tex]\rightarrow[/tex](0,0)f1(x,y)=0

c) is f1 contintoius at (0,0)?

## The Attempt at a Solution

f1=4x³/3(x

^{4}+y

^{4})

^{2/3}

along any line y=mx, it is 0, along y=x² I run into a problem, where i get 4x

^{1/3}/3(1+x

^{4})

^{2/3}, don't know what to do.

Once i pass this, I have a hunch i need to use squeeze theorm, yet I don't know how.

EDIT: realized that if I sub in 0 for x in the parabola limit, it goes to 0. I just need help organizing a squeeze theorem equivilent I am thinking [tex]\frac{4x^{3}}{3}[/tex]?

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