Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno
Options

Go back

Topic review (newest first)

scientia
2013-01-07 20:48:04

You're welcome. cool

anonimnystefy
2013-01-07 12:17:22

Wow! That is amazing! Thank you! smile

scientia
2013-01-07 11:51:08

bobbym wrote:



The above limit equals 1 / 2 . But the limit is very difficult to handle.


Consider the numerator (ignoring the minus sign outside the fraction). Notice that the terms in
and
vanish so the highest power of
is
. Its coefficient is
. Now look at the denominator. The highest power of
is also
and its coefficient is
. Hence the limit as
is



using the following rule:

If





and
and
then

bobbym
2013-01-07 11:42:20

Why do you think this is a job for Stoltz then?

anonimnystefy
2013-01-07 11:12:44

It wasn't hard.

I don't think ot would get much prettier...

bobbym
2013-01-07 11:04:05

You got that far! How the heck did you get there?


Maybe we can use Stolz again?

anonimnystefy
2013-01-07 10:58:08

I already got that much. That limit there is the problem...

bobbym
2013-01-07 10:14:58

I am trying to put it into the required form but the algebra is hideous.













The above limit equals 1 / 2 . But the limit is very difficult to handle.

anonimnystefy
2013-01-07 10:07:31

That is right.

bobbym
2013-01-07 09:57:02

We are not allowed to split that limit?

Probably not, the two pieces are both equal to infinity.

anonimnystefy
2013-01-07 09:54:32

Do you see the n/(p+1) part? It makes it not possible to use Stolz like that.

bobbym
2013-01-07 09:51:59









We need to use the binomial theorem here now.

anonimnystefy
2013-01-07 09:25:07

No. I already looked at that page. It just gets the limit to the indeterminate from 0*infinity...

bobbym
2013-01-07 09:12:31
anonimnystefy
2013-01-07 08:45:52

Hi

Can anyone help me with the following limit:



I know that it should be equal to 1/2 and the the Stolz theorem is supposed to be used, but I cannot get the final result...

Board footer

Powered by FluxBB