The Laplace Transform of a unit step function $${u_a}\left( t \right),$$ defined as
$$\matrix{ {{u_a}\left( t \right) = 0} & {for\,\,\,t < a\,} \cr { = 1} & {for\,\,\,t > a,} \cr } $$ is

The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

The Taylor's series expansion of sin $$x$$ is ______.

A discontinuous real function can be expressed as