Question

Lim [x]
x to 0 --- ?
x
where [x] is the Greatest integer function

Answer 1

what kinda function is that defined as, the one on top is the one i'm asking about?

Answer 2

Greatest integer function

Answer 3

is that one sided
or actual limit?

Answer 4

actual limit ? if it does not exist please give me the proper reason

Answer 5

it must be zero because a zero divided by any number whatever small has to be zero.

Answer 6

because greatest integer function of (x) =0 if 0<x<1
and
greatest integer function of (x)=-1 if -1<x<0

Suppose we had
\[\lim_{x \rightarrow 0^+}\frac{\lceil x \rceil}{x}=\lim_{x \rightarrow ^+}\frac{0}{x}=0\]
but look from the other side and see what you

Answer 7

you will see a cute surprise

Answer 8

Thank you sir.

Answer 9

\[\lim_{x \rightarrow 0^-}\frac{\lceil x \rceil}{x}\]

what will the greatest integer function(x) approach if we are looking to the left of 0?

Answer 10

inf

Answer 11

right 1 am i ?

Answer 12

perfect because we have -1/x

Answer 13

so limit does not exist.!!

Answer 14

and as x approaches 0 -1/x approaches inf
the limit does not exist
very good

Answer 15

i think that all made sense to you? :)

Answer 16

Yeah of course ..!!