The value of $$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}$$ is

If $$f(x) = \left\{ {\matrix{ {a{x^2} + 1,} & {x \le 1} \cr {{x^2} + ax + b,} & {x > 1} \cr } } \right.$$ is differentiable at x = 1, then