1. The problem statement, all variables and given/known data
lim (3/n)^2n
n→ ∞
2. Relevant equations
L'hopital's rule: lim F(a)/G(a) is indeterminate form, then the limit can be written as lim F'(a)/G'(a)
x → a x→ a
3. The attempt at a solution
lim e^[ln(3/n)^2n] = lim e^(2n * ln(3/n))
n→ ∞ n → ∞
2n * ln(3/n) = [2 * ln(3/n)] / n^-1 and applying L.h., [2 * (n/3) * (-3/n^2)]/(-n^-2)
reduces to, 2 * n, and clearly, plugging in n = infinity is wrong. Where did I go wrong, and what can I do to fix this problem?
lim (3/n)^2n
n→ ∞
2. Relevant equations
L'hopital's rule: lim F(a)/G(a) is indeterminate form, then the limit can be written as lim F'(a)/G'(a)
x → a x→ a
3. The attempt at a solution
lim e^[ln(3/n)^2n] = lim e^(2n * ln(3/n))
n→ ∞ n → ∞
2n * ln(3/n) = [2 * ln(3/n)] / n^-1 and applying L.h., [2 * (n/3) * (-3/n^2)]/(-n^-2)
reduces to, 2 * n, and clearly, plugging in n = infinity is wrong. Where did I go wrong, and what can I do to fix this problem?
via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=708142&goto=newpost
0 commentaires:
Enregistrer un commentaire