CA

Question

CA

iwanttogotostanford · Answer

@jango_IN_DTOWN @SolomonZelman @sooobored @retirEEd @mathmate @legomyego180 @inkyvoyd

solomonzelman · Answer

Intuitively ?

solomonzelman · Answer

let $P(n)$ denote a polynomial of degree $n$.
Then,

$\displaystyle \lim_{x\to \infty} \frac{P(n)}{P(n+1)}=0$.

solomonzelman · Answer

You can do L'H'S n times, to get a/bn.

solomonzelman · Answer

have you learned the L'Hospital's Rule?

solomonzelman · Answer

(I am trying to look for a relevantly light approach without intuition, or L'H'S ... and can't seem to come up with any for this kind of problem.)

solomonzelman · Answer

You can just tell me based on the fact that the bottom polynomial is cubic, and the top is only quadratic.    Or you can differentiate by L'Hospital's rule is you learned it.

solomonzelman · Answer

Basically, by intuition (or L'H'S)

$\color{black}{\displaystyle \lim_{x\to\infty}\frac{P(x)}{P(x+\alpha )}}=0$

$\color{black}{\displaystyle \lim_{x\to\infty}\frac{P(x+\alpha )}{P(x)}}=\pm \infty$
(Depending on the leading coefficients on top and bottom)

solomonzelman · Answer

Bye!

iwanttogotostanford · Answer

SO IT WOULD BE "B" CORRECT??

iwanttogotostanford · Answer

@3mar @HolsterEmission @mathmate @Nnesha @OtherWorldly

iwanttogotostanford · Answer

???

iwanttogotostanford · Answer

is it 0 or infinity???

3mar · Answer

Sorry, I was not here!