Given lim_(x->2) (2x-2) = -6, what is the best choice of d such that |(2x-2)-(-6)| < 0.03 whenever |x+2| < d?

Answer 1

I think you mean lim_(x -> -2)
You want

|(2x-2)-(-6)| < 0.03
|2x+4| < 0.03
|x+2| < 0.015

Answer 2

Yep.
I've gone to the point -2.015<x<-1.985, because -0.03<2x+4<0.03 and you solve from that point on. But what do I choose to get d?

Answer 3

well, duh. d = 0.015
look at what I wrote.