If f is differentiable at x = a, find the value of $$\mathop {\lim }\limits_{x \to a} {{{x^2}f(a) - {a^2}f(x)} \over {x - a}}$$

If $${{dy} \over {dx}} + \sqrt {{{1 - {y^2}} \over {1 - {x^2}}}} = 0$$, prove that $$x\sqrt {1 - {y^2}} + y\sqrt {1 - {x^2}} = A$$, where A is a constant.

Find the general solution of $$(x + \log y)dy + y\,dx = 0$$