Stuck trying to finding the Value of Delta in this problem

[andresfm92]

I've gotten to the point in finding that L is equal to 0, when plugging in 8 into the equation. I simplified the function into |x-8||x+8|, I guess I'm just completely lost on trying to find the value of delta when approaching this problem the same way as I would other problems.

 

[HallsofIvy]

\(\displaystyle |x^2- 64|< 0.001\) is the same |(x- 8)(x+ 8)|< 0.001. If x is close to 8 then x+ 8 will be positive so we can write that as (x+ 8)|x- 8|< 0.001 and then |x- 8|< 0.001/(x+ 8). The largest value of a fraction, with fixed numerator, occurs when the denominator is smallest.