Let $$f\left( x \right) = {x^2} - 1,\,0 < x < 2$$ and $$2x + 3,\,2 \leqslant x < 3.$$ The quadratic equation whose roots are, $$\mathop {\lim }\limits_{x \to 2 - 0} f\left( x \right)$$ and $$\mathop {\lim }\limits_{x \to 2 + 0} f\left( x \right)$$ is :
If $$G\left( x \right) = - \sqrt {25 - {x^2}} $$ then $$\mathop {\lim }\limits_{x\, \to \,{\text{I}}} \frac{{G\left( x \right) - G\left( I \right)}}{{x - 1}}$$ has the value-
If $$\eqalign{
& f\left( x \right) = \frac{{\sin \left[ x \right]}}{{\left[ x \right]}},\,\,\left[ x \right] \ne 0 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\, = 0,\,\,\,\,\,\,\,\,\,\,\,\,\,\left[ x \right] = 0 \cr} $$
Where \[\left[ x \right]\] denotes the greatest integer less than or equal to $$x.$$ then $$\mathop {\lim }\limits_{x\, \to \,0} f\left( x \right)$$ equals