what do the brackets mean? $\lim _{n\rightarrow \infty }{n}^{3/2}[\sqrt {{n}^{3}+3}-\sqrt {{n}^{3} -3}] $ Calculate: $\lim _{n\rightarrow \infty }{n}^{3/2}[\sqrt {{n}^{3}+3}-\sqrt {{n}^{3}
-3}]$

What do the brackets mean? I know sometimes they are used to denote a function that returns only the integer part of a number, like $f(x) = [x]$  has values of $0$ on $(0,1)$ and then jumps to $1$ on [1,2) and then $2$ on $[2,3)$ and so on...
Is this what is meant here? 
 A: Here the brackets are equivalent to $($ $)$. I am saying so because we don't usually use the integer part function in a calculus or analysis context. If you are in a number theory context, then those might mean the integer part function, but then I don't see why you would be computing this limit.
Hope that helps,
A: It is unlikely to be integer part, as that would make the $n^{3/2}$ term irrelevant.
I am quite sure that it is the normal brackets: ().
A: Or, using the binomial theorem,
${n}^{3/2}(\sqrt {{n}^{3}+3}-\sqrt {{n}^{3}-3})
= n^3(\sqrt {1+3/n^3}-\sqrt {1-3/n^3})
$
$
= n^3((1 + 3/(2n^3) + O(1/n^6))
- (1 - 3/(2n^3) + O(1/n^6))
$
$
n^3(3/n^3 + O(1/n^6)
= 3 + O(1/n^3)
$.
A: The bracket function is denoted by [ ], and is defined as [x] is equal to the largest integer that is equal or less then x
For Example 
   (1)  [5.5]=5
   (2)  [-0.1]=-1
   (3)  [-1.9]=-2
A: The bracket function $[x]$ means the greatest value of $x$. For example: If we put $x = 5.5$ then the value returned by this function will be $x = 5$. Let's see $[5.5] = 5$ because the greatest integer is $5$.
