- #1
bodensee9
- 178
- 0
Hi,
can I do the following?
If I am asked to find as lim x -> inf of (3^n/2^n), can I do:
3^n = e^(n*ln3)
2^n = e^(n*ln2)
assume C = lim (3^n/2^n).
C = lim e^(n*ln3)/e^(n*ln2)
ln C = lim ln [(exp(n*ln3)/(exp(n*ln2)]
In C = lim ln(exp(n*ln3)) - ln(exp(n*ln2))
ln C = lim n*ln3 - n*ln2
ln C = lim n*(ln3 - ln2)
The right hand side is clearly inf, and hence ln C = inf, which would mean that C = inf?
Though wouldn't C = 0 also give you infinity? So how would I know which one it is?
Thanks.
can I do the following?
If I am asked to find as lim x -> inf of (3^n/2^n), can I do:
3^n = e^(n*ln3)
2^n = e^(n*ln2)
assume C = lim (3^n/2^n).
C = lim e^(n*ln3)/e^(n*ln2)
ln C = lim ln [(exp(n*ln3)/(exp(n*ln2)]
In C = lim ln(exp(n*ln3)) - ln(exp(n*ln2))
ln C = lim n*ln3 - n*ln2
ln C = lim n*(ln3 - ln2)
The right hand side is clearly inf, and hence ln C = inf, which would mean that C = inf?
Though wouldn't C = 0 also give you infinity? So how would I know which one it is?
Thanks.