- #1
CalculusSandwich
- 18
- 0
Ok, so I have the problem lim n-> infinity (1 +5/n)^(4n)
So looking at it without trying anything I can see for n arbitrarily large 5/n goes to 0. That means (1+0)^(infinity). One to the power of any real number is one. However by looking at the definition of e as x->infinity I can say (1+ 1/x)^x=e^1
So (1+5/x)^(4x)= e^5*4 or e^20, which is not quite one. Where am I going wrong here?
Also I have the problem lim n-> infinity (n/n+3)^2n . I can same the same thing here as n tends to go to infinity I would have infinity over infinity which is 1? so one raised to infinity is one. I know I am incorrect in this assumption but why?
How would I go on solving this problem?
LIM N-> infinity
(N/N+3)^(2N) =
So looking at it without trying anything I can see for n arbitrarily large 5/n goes to 0. That means (1+0)^(infinity). One to the power of any real number is one. However by looking at the definition of e as x->infinity I can say (1+ 1/x)^x=e^1
So (1+5/x)^(4x)= e^5*4 or e^20, which is not quite one. Where am I going wrong here?
Also I have the problem lim n-> infinity (n/n+3)^2n . I can same the same thing here as n tends to go to infinity I would have infinity over infinity which is 1? so one raised to infinity is one. I know I am incorrect in this assumption but why?
How would I go on solving this problem?
LIM N-> infinity
(N/N+3)^(2N) =