hi,
correct me if i'm wrong:
|X^4-16|= |(X+2)(X-2)(X^2+4)|
|X-2|=|X+2-4|<|X+2|+|-4|
we let delta less then 1
|X+2|< 1
|X-2| < (3)+(4) = 7
|X^2-4+8|<|(X+2)(X-2)+8|<|X+2||X-2|+|8| = (1)(5)+8 =13
from here,
|X^4-16|= |(X+2)(X-2)(X^2+4)|< delta(7)(13) = 91 delta
91 delta = epsilon
delta = epsilon/91.
We chose the min delta {1, epsilon/91}