If a function is continuous at a point,

The value of the definite integral $$\int_1^e {\sqrt x \ln \left( x \right)dx} $$ is

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

Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is