If $$y = 2{x^3} - 2{x^2} + 3x - 5$$, then for x = 2 and $$\Delta$$x = 0.1 the value of $$\Delta$$y is

The approximate value of $$\root 5 \of {33} $$ correct to 4 decimal places is

Let $$f(x) = {x^3}{e^{ - 3x}},\,x > 0$$. Then the maximum value of f(x) is

Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{ 1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr {e^{({x^{10}} - 1)}} + {(x - 1)^2}\sin {1 \over {x - 1}},\,\mathrm{if}\,x \ne 1 \hfill \cr} \right.$$

then