Question

ques

Answer 1

Given:
\[0<|x-a|<\delta\] -(1)
and to prove
\[|x-a|<f(\epsilon)\]
Let
\[\delta=f(\epsilon)\]
(1) becomes
\[0<|x-a|<f(\epsilon)\]
\[\implies |x-a|<f(\epsilon)\]
\[\implies |x-a|<f(\epsilon) \iff \delta=f(\epsilon)\]
Is this correct?

Answer 2

thanks