- #1
aclark609
- 35
- 1
My question has to do with Euler's constant towards the end of the proof:
d/dx ln/x = lim h → 0 1/h ln(x+h) - lnx
= lim h→0 1/h ln[(x+h/x]
= lim h→0 1/h ln(1 + h/x)
= lim h→0 ln(1 + h/x)^(1/h)(1/x)(x/1)
= lim h→0 1/x ln(1+h/x)^(x/h) ;
let u = x/h
= 1/x lim h→0 ln(1+1/u)^u
= 1/x lne
= 1/x
Doesn't Euler's constant deal with the lim h→∞ instead of 0? Are they interchangeable? If so, why?
d/dx ln/x = lim h → 0 1/h ln(x+h) - lnx
= lim h→0 1/h ln[(x+h/x]
= lim h→0 1/h ln(1 + h/x)
= lim h→0 ln(1 + h/x)^(1/h)(1/x)(x/1)
= lim h→0 1/x ln(1+h/x)^(x/h) ;
let u = x/h
= 1/x lim h→0 ln(1+1/u)^u
= 1/x lne
= 1/x
Doesn't Euler's constant deal with the lim h→∞ instead of 0? Are they interchangeable? If so, why?