$\lim _{x \rightarrow 0^{+}} \frac{[x]}{\tan x}$ where $[x]$ is the greatest integer function
[list=1]
[*] -1
[*] 0
[*] 1
[*] Does not exists
[/list]
1. We need to evaluate the limit $\lim_{x \rightarrow 0^{+}} \frac{[x]}{\tan x}$, where $[x]$ is the greatest integer function (also known as the floor function).
2. The greatest integer function $[x]$ returns the largest integer less than or equal to $x$. For $0 < x < 1$, $[x] = 0$ because $x$ is a positive number less than 1.
3. Therefore, for $0 < x < 1$, we have:
   \[
   \frac{[x]}{\tan x} = \frac{0}{\tan x} = 0
   \]
4. Since $\tan x$ is continuous and non-zero for $0 < x < 1$, the expression $\frac{0}{\tan x}$ remains 0 as $x$ approaches 0 from the right.
5. Hence, the limit is:
   \[
   \lim_{x \rightarrow 0^{+}} \frac{[x]}{\tan x} = 0
   \]

The final answer is $\boxed{0}$