12th Class
Mathematics
Sample Paper
Maths Olympiad Model Test Paper-10
question_answer
If \[f(x)=\left| \begin{matrix} \cos x & x & 1 \\ 2\sin x & {{x}^{2}} & 2x \\ \tan x & x & 1 \\ \end{matrix} \right|\] then \[\underset{x\to 0}{\mathop{\lim }}\,\,\,\left[ \frac{f'(x)}{x} \right]\] is ________.