Question

1. Prove that If lim f(x) exist, then it is Unique.​

Answer 1

Answer:

The limit of a function is unique if it exists. f(x) = L2 where L1,L2 ∈ R. For every ϵ > 0 there exist δ1,δ2 > 0 such that 0 < |x − c| < δ1 and x ∈ A implies that |f(x) − L1| < ϵ/2, 0 < |x − c| < δ2 and x ∈ A implies that |f(x) − L2| < ϵ/2. ... We can rephrase the ϵ-δ definition of limits in terms of neighborhoods.