question_answer

The value of \[\underset{x\to 0}{\mathop{\lim }}\,\frac{{{27}^{x}}-{{9}^{x}}-{{3}^{x}}+1}{\sqrt{2}-\sqrt{1+\cos x}}\] is _______.  

A)  \[4\,\sqrt{2}\,{{(\log \,3)}^{2}}\]                      

B)  \[8\sqrt{2}\,{{(\log \,3)}^{2}}\]

C)  \[2\,\sqrt{2}\,{{(\log \,3)}^{2}}\]                      

D)  \[3\,\sqrt{2}\,{{(\log \,3)}^{2}}\]

E)  None of these