Question

Find the largest number δ such that if |x − 1| < δ, then |5x − 5| < ε, where ε = 0.1. δ ≤ repeat and determine δ with ε = 0.01.

Answer 1

$|5x-5|=5|x-1|$

So for $\varepsilon=0.1$, we get $\delta=50$; for $\varepsilon=0.01$, we get $\delta=500$.