The determinant of matrix $$A$$ is $$5$$ and the determinant of matrix $$B$$ is $$40.$$ The determinant of matrix $$AB$$ is _______.

The maximum value of the determinant among all $$2 \times 2$$ real symmetric matrices with trace $$14$$ is ______.

For $$0 \le t < \infty ,$$ the maximum value of the function $$f\left( t \right) = {e^{ - t}} - 2{e^{ - 2t}}\,$$ occurs at

The value of $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^x}\,\,$$ is