Question

lim x->infinity for ln6x/e^5x

Answer 1

inf/inf invokes Lhpoital

Answer 2

L'Hopital

Answer 3

\[\lim x \rightarrow \infty \ln6x/e ^{5x}\]

Answer 4

take the derivative of the top and bottom, don't use product rule

Answer 5

0

Answer 6

to apply L'H rule

Answer 7

ln(6x) = ln(6) + ln(x) by the way

Answer 8

are you asking this \[\lim_{x \rightarrow \infty}\frac{\ln 6x}{e^{5x}}\]

Answer 9

\[e^{5x}>>\ln(6x)\]

Answer 10

\[\frac{1/inf=0}{5e^{5inf}=inf}\]
either way you go you get to 0

Answer 11

also notice that e^5x grows alot faster than ln(6x) so it over powers it

Answer 12

1/1000000000 is a good visual; which is very very tiny