Let $f\left(x\right)=\underset{m\to \infty }{\lim }\left\{\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\mathrm{.....}\sqrt[n]{e^{{\sin }^{2}x}}}}}}\right\}$ where  $n={\sec }^{2}x$  and  given m is the number of radicals in   $\left\{\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\sqrt[n]{e^{{\sin }^{2}x}\mathrm{.....}\sqrt[n]{e^{{\sin }^{2}x}}}}}}\right\}$ ,
then select INCORRECT alternative(s).
(Consider meaning of radical as  $\sqrt[n]{z}=z^{\frac{1}{n}}\forall n\in R^{+}$ )

The number 1 is in the range of function  $f\left(x\right)$  and it is the minimum value of the function

The function is unbounded

The number e is in the range of the function, and it is the maximum value  of the function.

There is only one integer in the range of  $f\left(x\right)$