- #1

idochemistry

- 6

- 0

## Homework Statement

Find a specific number δ>0 such that if x

^{2}+ y

^{2}= δ

^{2}, then |x

^{2}+y

^{2}+3xy+180xy

^{5}< 1/10 000.

Answer: Choose δ < 0.002

## Homework Equations

ε-δ def'n of limit: lim (x,y) → (a, b) f(x) = L if for every ε > 0 there exists a δ > 0 such that 0 < √(x-a)

^{2}+(y-b)

^{2}, |f(x) - L| < ε.

## The Attempt at a Solution

So, f(x) = |x

^{2}+y

^{2}+3xy+180xy

^{5}and because x

^{2}+ y

^{2}= δ

^{2}, the limit is being taken as (x, y) → (0, 0) and L = 0.

I don't understand how I would start this problem because it's not rational, like I'm used to. I can do this:

(x) = |x

^{2}+y

^{2}+3xy+180xy

^{5}= x

^{2}+ y

^{2}+ 3|x||y| + 180|x||y

^{5}|, but now I am stuck. Any help is greatly appreciated.