Let f(x + y) = f(x) f(y) and f(x) = 1 + xg(x) $$\phi$$ (x), where $$\mathop {\lim }\limits_{x \to 0} $$ g(x) = a and $$\mathop {\lim }\limits_{x \to 0} $$ $$\phi$$ (x) = b. Then, what is f'(x) equal to ?

What is $$\mathop {\lim }\limits_{x \to {\pi \over 6}} {{2{{\sin }^2}x + \sin x - 1} \over {2{{\sin }^2}x - 3\sin x + 1}}$$ equal to ?

Consider the function $$f(x) = \left\{ {\matrix{ {{x^2}In|x|} & {x \ne 0} \cr 0 & {x = 0} \cr } } \right.$$ What is f' (0) equal to ?

If $$f(x) = {{{x^2} - 9} \over {{x^2} - 2x - 3}},x \ne 3$$ is continuous at x = 3, then which one of the following is correct?