In which of the following functions, Rolle's theorem is applicable?

The value of $$\mathop {\lim }\limits_{x \to 1} {{x + {x^2} + ..... + {x^n} - n} \over {x - 1}}$$ is

$$\mathop {\lim }\limits_{x \to 0} {{\sin (\pi {{\sin }^2}x)} \over {{x^2}}} = $$

If the function $$f(x) = \left\{ {\matrix{ {{{{x^2} - (A + 2)x + A} \over {x - 2}},} & {for\,x \ne 2} \cr {2,} & {for\,x = 2} \cr } } \right.$$ is continuous at x = 2, then