question_answer

If \[\left| \begin{matrix}    \tan \,x & \tan (x+h) & \tan (x+2h)  \\    \tan (x+2h) & \tan x & \tan (x+h)  \\    \tan (x+h) & \tan (x+2h) & \tan x  \\ \end{matrix} \right|\], then the value of \[\underset{h\to 0}{\mathop{\lim }}\,\frac{\Delta (\pi /4)}{{{h}^{2}}}\] is

A) 36               

B) 81                    

C) 144                         

D) 256

Correct Answer: A

Solution :

    [a] \[\frac{\Delta }{{{h}^{2}}}=\left| \begin{matrix}    \tan x & \frac{\tan (x+h)-\tan x}{h} & \frac{\tan (x+2h)-\tan x}{h}  \\    \tan (x+2h) & \frac{\tan x-\tan (x+2h)}{h} & \frac{\tan (x+h)-\tan (x+2h)}{h}  \\    \tan (x+h) & \frac{\tan (x+2h)-tan(x+h)}{h} & \frac{\tan x-\tan (x+h)}{h}  \\ \end{matrix} \right|\]