The number of discontinuities of the greatest integer function $$\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)$$

$$\matrix{ {f(x) = a{x^2} + bx + 1,} & {if} & {\left| {2x - 3} \right| \ge 2} \cr { = 3x + 2,} & {if} & {{1 \over 2} < x < {5 \over 2}} \cr } $$

is continuous on its domain, then $$a+b$$ has the value

If $$\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5$$, then $$(a+b)$$ is equal to

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1-\cos x^2}}{1-\cos x}=$$