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.

[tex]|5x-5|=5|x-1|<\varepsilon\implies|x-1|<\dfrac\varepsilon5=\delta[/tex]

So for [tex]\varepsilon=0.1[/tex], we get [tex]\delta=50[/tex]; for [tex]\varepsilon=0.01[/tex], we get [tex]\delta=500[/tex].