If a real valued function $f(x)=\left\{\begin{array}{cl}e^{\frac{\sin a(x-[x])}{x-[x]}} & , \text { if } x<1 \\ b+1 & , \text { if } x=1 \text { is } \\ \frac{\left|x^2+x-2\right|}{x-1} & , \text { if } x>1\end{array}\right.$ continuous at $x=1$, then $b \sin a=([x]$ denotes the greatest integer function)

$$\mathop {\lim }\limits_{x \to {\pi \over 4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x}= $$

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,

$$ \lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)= $$

If the function $f$ defined by

$$ f(x)=\left\{\begin{array}{cc} \frac{1-\cos 4 x}{x^2}, & x<0 \\ a, & x=0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & x>0 \end{array}\right. $$

is continuous at $x=0$, then $a=$