For the function $$f(x) = {e^{\cos x}}$$, Rolle's theorem is

$$f(x) = \left\{ {\matrix{ {0,} & {x = 0} \cr {x - 3,} & {x > 0} \cr } } \right.$$

The function f(x) is

The function f(x) = ax + b is strictly increasing for all real x if

$$ \text { Let } f(x)=\left|\begin{array}{ccc} \cos x & x & 1 \\ 2 \sin x & x^3 & 2 x \\ \tan x & x & 1 \end{array}\right| \text {, then } \lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}= $$