Let m and n be two positive integers greater than 1. If $$$\mathop {\lim }\limits_{\alpha \to 0} \left( {{{{e^{\cos \left( {{\alpha ^n}} \right)}} - e} \over {{\alpha ^m}}}} \right) = - \left( {{e \over 2}} \right)$$$ then the value of $${m \over n}$$ is _________.

The largest value of the non-negative integer a for which $$\mathop {\lim }\limits_{x \to 1} {\left\{ {{{ - ax + \sin (x - 1) + a} \over {x + \sin (x - 1) - 1}}} \right\}^{{{1 - x} \over {1 - \sqrt x }}}} = {1 \over 4}$$ is

Let f : R $$\to$$ R and g : R $$\to$$ R be respectively given by f(x) = | x | + 1 and g(x) = x² + 1. Define h : R $$\to$$ R by $$h(x) = \left\{ {\matrix{ {\max \{ f(x),g(x)\} ,} & {if\,x \le 0.} \cr {\min \{ f(x),g(x)\} ,} & {if\,x > 0.} \cr } } \right.$$

The number of points at which h(x) is not differentiable is