Let a⊆r, let f: a⟶r and let c∈r be a cluster point of a. if lim┬(x⟶c)⁡f exists, and if |f| denotes the function defined for x∈a by |f|(x)≔|f(x)|, prove that |lim┬(x⟶c) |⁡f |=|lim┬(x⟶c)⁡|f|

Answer with Step-by-step explanation:

We are given that

Let f:

be  a cluster point of A.

exist let

If denotes the function and

for

We have to prove that

Substitute the value then we get

Hence proved.

answer: what is the question you're trying to ask?

step-by-step explanation: