Find the largest number δ such that if |x − 4| < δ, then |4x − 16| < ε, where ε = 1. δ

Question

Find the largest number δ such that if |x − 4| < δ, then |4x − 16| < ε, where ε = 1.

δ ≤ ______

Repeat and determine δ with ε = 0.1.

δ ≤ ______

Answer 1

Because |4x − 16| < ε; so, 4|x − 4| < ε, |x − 4| < ε/4 =1/4.

Comparing with |x − 4| < δ we get 0 < δ ≤ 1/4

If ε = 0.1 then max δ = 0.1/4 = 0.025