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Posted by **Help!!** on Saturday, December 1, 2012 at 9:27pm.

- calculus -
**Damon**, Saturday, December 1, 2012 at 9:54pmx = 1

f = (14/17)^4 = .46

x = 10

f = (140/143)^40 = .428

x = 100

f = (1400/1403)^400 = .4248

x = 1000

f = (14,000/14,003)^4000 = .4244

hmmm

- calculus -
**Damon**, Saturday, December 1, 2012 at 10:01pmx = 10,000

f = (140,000/140,003)^40,000 = .4244

double hmmm

- calculus -
**Damon**, Saturday, December 1, 2012 at 10:03pmx = 100,000

f = (1,400,000/1,400,003)^400,000 = .4244

- calculus -
**Count Iblis**, Saturday, December 1, 2012 at 10:45pmLog[f(x)] =

4 x [log(14 x) - log(14 x + 3)] =

-4 x log[1 + 3/(14 x)] =

-4 x [3/(14 x) + O(1/x^2)] =

-6/7 + O(1/x)

The limit for x to infinity of

log[f(x)] is thus -6/7, the limit of

f(x) is thus exp(-6/7)

- calculus -
**Help!!**, Sunday, December 2, 2012 at 2:58pmWhat happened between

-4 x log[1 + 3/(14 x)] =

and

-4 x [3/(14 x) + O(1/x^2)] =

How did you get rid of the log? Thx in advance