If $$f(x) = \sqrt {25 - {x^2}} $$, then what is $$\mathop {\lim }\limits_{x \to 1} {{f(x) - f(1)} \over {x - 1}}$$ equal to ?

What is $$\mathop {\lim }\limits_{\theta \to 0} {{\sqrt {1 - \cos \theta } } \over \theta }$$ equal to ?

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 ?