$$\,\mathop {Lim}\limits_{x \to 0} \left( {{{1 - \cos x} \over {{x^2}}}} \right)$$ is

At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has

If $$f(x)$$ is even function and a is a positive real number , then $$\int\limits_{ - a}^a {f\left( x \right)dx\,\,} $$ equals ________.

A series expansion for the function $$\sin \theta $$ is _______.