Question

lim (x->infinity) (log x/x^p)
where p belongs to real no.

Answer 1

is
\[p>0\]?

Answer 2

is it \(\log\frac{x}{x^p}\) ?

Answer 3

you really need to know this because for example if
\[p=-5\] you have
\[x^5\times log(x)\] whereas if

\[p=5\] you have
\[\frac{\log(x)}{x^5}\]

Answer 4

i am willing to bet that somewhere it says that
\[p>0\] and then the limit will be zero.
otherwise you really have no idea right?

Answer 5

sorry i was just busy wid some other work......

actualy that is the problem that it is not given whether p is +ve or _ve or fraction...
otherwise it is a very simple question.....

Answer 6

and also if p>0 ,then also there is a problem....if it is a fraction then answer will be different..

Answer 7

why don't you differentiate it for p>0 limit would be zero only ...

Answer 8

I mean apply l'hospital

Answer 9

I am not sure though

Answer 10

if p is fraction then?

Answer 11

i don't think that would make a difference anything to the power of infinity should be infinity only

Answer 12

if p is fraction then after differenciating power of x will be negative..at denominator....so it will become infinity...

Answer 13

hmm okay then you solve this for three cases when p <0 , 0<p<1 and p>1

Answer 14

or solve it for p<1 and p>1

Answer 15

but i think for p<0 it will be -infinity and for 0<p<1 it is +infinity...

Answer 16

well if you are not given the sign of p there is no answer. unless you are supposed to say "it depends on whether p is positive or negative, because you get a different limit in each case"

Answer 17

we can make cases...