If \[f(x)\,=\left| \,\begin{matrix} \sin x & \cos x & \tan x \\ {{x}^{3}} & {{x}^{2}} & x \\ 2x & 1 & 1 \\ \end{matrix}\, \right|\], then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{{{x}^{2}}}\] is [Karnataka CET 2002]

If \[f(x)\,=\left| \,\begin{matrix} \sin x & \cos x & \tan x \\

1.	If \[f(x)\,=\left\| \,\begin{matrix} \sin x & \cos x & \tan x \\ {{x}^{3}} & {{x}^{2}} & x \\ 2x & 1 & 1 \\ \end{matrix}\, \right\|\], then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{{{x}^{2}}}\] is [Karnataka CET 2002]
A.	3
B.	?1
C.	0
D.	1
Answer» E.

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If \[f(x)\,=\left| \,\begin{matrix} \sin x & \cos x & \tan x \\ {{x}^{3}} & {{x}^{2}} & x \\ 2x & 1 & 1 \\ \end{matrix}\, \right|\], then \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{{{x}^{2}}}\] is [Karnataka CET 2002]

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