Question

what is the limit of LN x / x

Answer 1

use l'hopital's rule to get 0

Answer 2

for x=zero this function is undefined

Answer 3

fraction with denominator zero ... interesantly

Answer 4

sorry .. i thought the limit was to infinity.

Answer 5

evern indifferent when we have one equation with fraction the first condition, substitution is that the denominator not can being zero

Answer 6

may be it is like this..lim [ x - ln(x) ]
x -> infinity

As you already know, this is in the form infinity - infinity, so we have to change its form.

One thing you can do is change the form of x to ln(e^x), because ln and e are inverses of each other and x = ln(e^x).

lim [ ln(e^x) - ln(x) ]
x -> infinity

Now, we can combine the logs as per the identity.

lim [ ln( e^x / x ) ]
x -> infinity

And we can move the limit inside the log.

ln [ lim (e^x / x ) ]
. . . x -> infinity

And now we can apply L'Hospital's rule.

ln [ lim ( e^x / 1 ) ]
. . . x -> infinity

ln [ lim ( e^x ) ]
. . . x -> infinity

As x approaches infinity, e^x approaches infinity.
As e^x approaches infinity, so does ln(e^x).
Therefore, the answer is infinity.

Answer 7

^ wasnt what the question was asking for , but something a little different

Answer 8

the limit does not exist! lol

i just remembered the movie of lindsay lohan "mean girls"
just sharing. hahaha