Given a function $$f\left( {x,y} \right) = 4{x^2} + 6{y^2} - 8x - 4y + 8,$$ the optimal values of $$f(x,y)$$ is

The function $$f\left( x \right) = 2{x^3} - 3{x^2} - 36x + 2\,\,\,$$ has its maxima at

Limit of the following sequence as $$n \to \infty $$ $$\,\,\,$$ is $$\,\,\,$$ $${x_n} = {n^{{1 \over n}}}$$

The value of the following improper integral is $$\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.$$