>>10954175(c^1/n-e)^n for very small e converges to c-ne*(c^(n-1)/n). This follows from polynominal expansion and ignoring all higher powers of e.
I will only deal with the lefthand side here.
c-ne*(c^(n-1)/n) < x -> -ne*(c^(n-1)/n) < x-c
or ne*(c^(n-1)/n) < |x-c|
The relationship between epsilon and delta is.
ne*(c^(n-1)/n) = d
or e = d*c^n/(n-1)/n
for any finite n, n*(c^(n-1)/n) is finite too. For big n, it converges to n*c.
