Question

lim (1 + 1/x)^(3x) as x->infinity

solving this using L'hopital's rule for indeterminate infinity - infinity.

Answer 1

lim ln([(x+1)/x]^3x) as x ->.infinity =
lim ln([(x+1)^(3x)]/[x^(3x)]) as s->infinity =
lim ln((x+1)^(3x))-ln(x^(3x)) = infinity - infinity

is this a correct start?

Answer 2

Don't worry this is only calc 2

Answer 3

you should probably just recognize this number

Answer 4

\[\lim_{x\to \infty}(1+\frac{1}{x})^x=e\]

Answer 5

and so your answer is \(e^3\) but you can use l'hopital if you like
take the log, get
\[3x\ln(1+\frac{1}{x})\]which is in the form \(\infty\times 0\) then use the usual trick of rewriting as
\[\frac{\ln(1+\frac{1}{x})}{\frac{1}{3x}}\]and use l'hopital for this one

Answer 6

in answer to your question, no, that was not the correct start

Answer 7

ah thank you

Answer 8

yw