Question

\[\lim_{x \rightarrow \infty} \frac{ \ln x^n-[x] }{ [x] }\]

Answer 1

what do you mean by [x] ??

Answer 2

greatest integer function

Answer 3

this is -1 ... isn't it obvious.

Answer 4

how ? can u explain

Answer 5

polynomial function always exceeds logarithmic function, the first part is zero ... the later part gives -1

Answer 6

log(x)/[x] -> 0 as x->infty

Answer 7

polynomial function always exceeds logarithmic function? how

Answer 8

i'll just show
log(x)/[x] -> 0 as x->infty