If $n$ is an integer,then $\mathop {\lim }\limits_{x \to n + 0} (x - [x]) = $

The value of $\lim _{x \rightarrow 0} \frac{x}{|x|+x^2}$ is .

The value of $\lim _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}$ is equal to

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

$\mathop {\lim }\limits_{x \to \infty } \frac{{(2x - 3)(3x - 4)}}{{(4x - 5)(5x - 6)}} = $

$\mathop {\lim }\limits_{x \to {a^ + }} \left( \frac{{|x{|^3}}}{a} - {\left[ {\frac{x}{a}} \right]^3} \right) \,(a > 0)$ is equal to :- (where $[x]$ is the greatest integer function and $|x|$ is the modulus function)