lim x→2 (6x + 2). Find the largest δ > 0 such that |f(x) − L| < 0.01 whenever 0 < |x − c| < δ. (Round your answer to four decimal places.)

Answer 1

f(x) = 6x + 2

f(2) = 14

Given ε > 0. Let δ = ε/6

If 0 < l x - 2 l < ε/6, then l 6x - 12 l < ε.

l (6x + 2) - 14 l < ε

l f(x) - f(2) l < ε

So,if ε = 0.01, then δ = ε/6 = 1/600