Question

lim as x approaches positive infinity of (1 + 1/4x) ^ 3x

Answer 1

make a guess, i bet it is right

Answer 2

if you guess wrong we can work through it

Answer 3

is it e or positive infinity??

Answer 4

closer with the \(e\) but not exactly \(e\) but rather \(e\) so some power

Answer 5

first off i assume it is
\[\lim_{x\to \infty}\left(1+\frac{1}{4x}\right)^{3x}\] right?

Answer 6

probably taught to "take the log" get
\[3x\ln(1+\frac{1}{4x})\] then it is in the form \(\infty\times 0\)
usual gimmick is to rewrite as
\[\frac{3\ln(1+\frac{1}{4x})}{\frac{1}{x}}\] then use l'hopital

Answer 7

would it be