If f(x) = left| begin{array}{ccc} sin x & cos | vedclass

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(D) Given $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & 	an x \ x^3 & x^2 & x \ 2x & 1 & x \end{array} ight|$.Expanding along the first row

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(D) Given $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & 	an x \ x^3 & x^2 & x \ 2x & 1 & x \end{array} ight|$.Expanding along the first row:$f(x) = \sin x(x^3 - x) - \cos x(x^4 - 2x^2) + 	an x(x^3 - 2x^4)$.We need to find $\lim_{x 	o 0} \frac{f(x)}{x^2}$.$\frac{f(x)}{x^2} = \frac{\sin x}{x} \cdot \frac{x^3 - x}{x} - \cos x \cdot \frac{x^4 - 2x^2}{x^2} + \frac{	an x}{x} \cdot \frac{x^3 - 2x^4}{x}$.$\frac{f(x)}{x^2} = \frac{\sin x}{x} (x^2 - 1) - \cos x (x^2 - 2) + \frac{	an x}{x} (x^2 - 2x^3)$.Taking the limit as $x 	o 0$:$= (1)(0 - 1) - (1)(0 - 2) + (1)(0 - 0)$.$= -1 + 2 + 0 = 1$.

If $f(x) = \left| \begin{array}{ccc} \sin x & \cos x & \tan x \\ x^3 & x^2 & x \\ 2x & 1 & x \end{array} \right|$,then $\lim_{x \to 0} \frac{f(x)}{x^2}$ is equal to

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