If $f(x)=\left\{\begin{array}{cc}\frac{a \sin x-b x+c x^2+x^3}{2 \log (1+x)-2 x^3+x^4} & , x \neq 0 \\ 0 & , x=0\end{array}\right.$

is continuous at $x=0$, then

If the function $g(x)=\left\{\begin{array}{cl}K \sqrt{x+1} & , 0 \leq x \leq 3 \\ m x+2 & , 3 < x \leq 5\end{array}\right.$ is differentiable, then $K+m=$

If $[x]$ is the greatest integer function, then

$$ \mathop {\lim }\limits_{x \to 3} \frac{(3-|x|+\sin |3-x|) \cos [9-3 x]}{|3-x|[3 x-9]} $$

Let ' $a$ ' be a positive real number. If a real valued function

$f(x)=\left\{\begin{array}{cl}\frac{6^x-3^x-2^x+1}{1-\cos \left(\frac{x}{a}\right)} & \text { if } x \neq 0 \\ \log 3 \log 4 & \text { if } x=0\end{array}\right.$ is continuous at $x=0$, then $a=$