The value of $$\mathop {\lim }\limits_{x \to 0} {{{{\sin }^2}x + \cos x - 1} \over {{x^2}}}$$ is

The value of $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + 5{x^2}} \over {1 + 3{x^2}}}} \right)^{{1 \over {{x^2}}}}}$$ is

If $$f(5) = 7$$ and $$f'(5) = 7$$, then $$\mathop {\lim }\limits_{x \to 5} {{x\,f(5) - 5f(x)} \over {x - 5}}$$ is given by

If $$y = (1 + x)(1 + {x^2})(1 + {x^4})\,.....\,(1 + {x^{2n}})$$, then the value of $${\left( {{{dy} \over {dx}}} \right)_{x = 0}}$$ is