Interesting limit: $$ \large \lim \limits_{x\to \infty} \frac{e^{px}}{x^{100}} $$

Question

Interesting limit: $$ \large  \lim \limits_{x\to \infty} \frac{e^{px}}{x^{100}} $$

lgbasallote · Answer

it's 0! lol

anonymous · Answer

Nopes.

anonymous · Answer

Assume p as +ve ;-)

lgbasallote · Answer

this is inf/inf...let's do LH >:))

e^px(p)/100x^99

still no good...

p^2e^px/9900x^98

still no good...

this is the circle i have always hated >.<

anonymous · Answer

Igb I choose this example to show you how to take care of things when L'Hop circles ;)

jamesj · Answer

You're not in a circle.  Just do it 100 times

lgbasallote · Answer

i cannot find any manipulation here @_@ this is really good

jamesj · Answer

Apply l'Hopital 100 times and you have
$$ \frac{p^100}{100!} e^{px} $$

jamesj · Answer

$$ \frac{p^{100}}{100!}e^{px} $$

anonymous · Answer

but there is a smarter way ...

lgbasallote · Answer

show us oh fool

anonymous · Answer

lol, think for sometime Igb :)

jamesj · Answer

Just tell us.

lgbasallote · Answer

i have thought and i have shared my thoughts.

lgbasallote · Answer

now it is time you taught us what you have thought

anonymous · Answer

$$ \large  \lim \limits_{x\to \infty} \frac{e^{px}}{x^{100}} = \left( \lim \limits_{x\to \infty} \frac{e^{\frac{px}{100}}}{x} \right)^{100} $$

Now apply L'Hop ...

anonymous · Answer

and you  will get your answer $ \infty $

nenadmatematika · Answer

just to get involved is p parameter in R?

jamesj · Answer

I'd like a refund on this one.

nenadmatematika · Answer

if p>0 than the limit is infinity and if <0 it's zero

hoblos · Answer

ffm do you know thayler's formula?

anonymous · Answer

No, not even google http://www.google.co.in/search?q=thayler%27s+formula&nfpr=1&ie=UTF-8&sourceid=chrome&btnG=Search

anonymous · Answer

or do you mean taylor's formula?

hoblos · Answer

lol yeah that one... you can use it

anonymous · Answer

Yes I know, but I think the way I showed above is easier ...