anonymous: please include name/email: correct (sjm1 AT williams.edu)
Steven Milleron September 19, 2012 at 5:55 am
Jimmy: well done (sjm1 AT williams.edu)
Steven Milleron July 24, 2012 at 3:13 am
I don’t understand: if x tends to infinity how can x tend to 1? email me at sjm1 AT williams.edu
Terryon July 23, 2012 at 9:19 am
As I’m doing this on my phone please forgive typos and lack of proper notation. As x tends toward infinity then the answer tends toward 1. So the limit of x^x^x = 2 as x tends to infinity is x tending toward 1. Isn’t it??
Steven Milleron April 2, 2012 at 8:06 pm
Your parentheses are off; if x = 1 + 1, then it is (1+1)^( (1+1)^(…) …).
lolon April 2, 2012 at 8:03 pm
no it won’t (1+1^(1+1^(1+1^(1+1…….)…) will equal 2, since 1 + 1^anything = 2.
Steven Milleron April 2, 2012 at 7:47 pm
Nope — that will give too big an answer //s
lolon April 2, 2012 at 7:26 pm
x = 1+1??
Steven Milleron December 31, 2011 at 3:29 am
Anon: you’re close but not quite there — email me at [email protected] if you want to discuss more.
Anonon December 31, 2011 at 2:59 am
let a^x = x^(x^(x^(x^…))…)
so a^x = 2
Take logs of both sides.
ln(a^x) = ln(2)
x*ln(a) = ln(2)
x = ln(2)/ln(a)
But since a is x to the power of x an infinite number of times, a = 2. So ln(a) = ln(2).
anon — yes — [email protected]
anonymous: please include name/email: correct (sjm1 AT williams.edu)
Jimmy: well done (sjm1 AT williams.edu)
I don’t understand: if x tends to infinity how can x tend to 1? email me at sjm1 AT williams.edu
As I’m doing this on my phone please forgive typos and lack of proper notation. As x tends toward infinity then the answer tends toward 1. So the limit of x^x^x = 2 as x tends to infinity is x tending toward 1. Isn’t it??
Your parentheses are off; if x = 1 + 1, then it is (1+1)^( (1+1)^(…) …).
no it won’t (1+1^(1+1^(1+1^(1+1…….)…) will equal 2, since 1 + 1^anything = 2.
Nope — that will give too big an answer //s
x = 1+1??
Anon: you’re close but not quite there — email me at [email protected] if you want to discuss more.
let a^x = x^(x^(x^(x^…))…)
so a^x = 2
Take logs of both sides.
ln(a^x) = ln(2)
x*ln(a) = ln(2)
x = ln(2)/ln(a)
But since a is x to the power of x an infinite number of times, a = 2. So ln(a) = ln(2).
Therefore x = 1.
It’s not 2/3…. email me at [email protected] if you want a hint
2/3
There’s a very simple solution. Email me at [email protected] if you want the soln or a hint.
X = ∞√2
^That does not say infinity times root 2. I just don’t know how to type unicode for infinity root 2 or however it’s supposed to be said
To ANT: correct!
x=sqrt(2)
Nope — if x = 2 you end up getting infinity.
X = 2
It means the process continues. Take the limit of x, x^x, x^(x^x), x^(x^(x^x)), ….
what do the dots mean? can u email me and write out the whole question without simplifying it or shortening it