(Solved): (a) Find the largest number \( \delta \) such that if \( |x-1| ...

(a) Find the largest number \( \delta \) such that if \( |x-1|<\delta \), then \( |5 x-5|<\varepsilon \), where \( \varepsilon=0.1 \). \( \delta \leq \) (b) Repeat part (a) and determine \( \delta \) with \( \varepsilon=0.01 \). \( \delta \leq \)