Question

whats the hospital rule for ln 3x

Answer 1

is it 1/3?

Answer 2

drink plenty of fluids, stay out of the sun

Answer 3

lol thanks i havent been out too extremely hot

Answer 4

ahaha. Do you men l'Hospitals rule? Is this supposed to be the limit as x->infinity of ln(3/x)

Answer 5

i have this here: lim
x→
ln 3x

3x

Answer 6

x approaches infinity ln3x/\[\sqrt{3x}\]

Answer 7

so i dont know how i would compute that

Answer 8

\[\lim_{x\rightarrow\infty}\frac{\ln(3x)}{\sqrt{3x}}\]

Answer 9

is that it?

Answer 10

if so use no rule. get 0 from your eyeballs. log grows very slow, much slower than
\[\sqrt{x}\]

Answer 11

yes

Answer 12

you are of course welcome to use l'hopital if you like

Answer 13

get
\[\frac{1}{x}\times \frac{2\sqrt{x}}{3}\] and then get
\[\frac{2}{3\sqrt{x}}\] take the limit, get 0

Answer 14

ok so thats the final answers?

Answer 15

clear yes? derivative of
\[\ln(3x)\] is
\[\frac{1}{x}\] and derivative of
\[\sqrt{3x}\] is
\[\frac{3}{2\sqrt{x}}\]

Answer 16

yes answer is 0

Answer 17

yes thanks!