Consider the function g(x) = 1/x.
b. Find a number δ′ > 0 different from the number δ you found in the previous question such that all the values x ∈ (2 − δ′, 2 + δ′) satisfy that g(x) is within 0.1 of 1/2.
Note, I found I value δ>0 in an earlier question in which the values x∈(2−δ,2+δ) satisfy that g(x) is within 0.1 of 1/2. That value of δ=1/10.
This question b. practically asks the same thing, but for a different value δ'.
The Attempt at a Solution
Now, I'm considering since we know δ=1/10, then 0<δ'<δ=1/10. Any value of δ' in this interval will satisfy the conditions in question. But how would I show this, more formally.