A) 3
B) ?1
C) 0
D) 1
Correct Answer: D
Solution :
\[f(x)=x(x-1)\sin x-({{x}^{3}}-2{{x}^{2}})\cos x-{{x}^{3}}\tan x\] \[={{x}^{2}}\sin x-{{x}^{3}}\cos x-{{x}^{3}}\tan x+2{{x}^{2}}\cos x-x\sin x\] Hence \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)}{{{x}^{2}}}=\underset{x\to 0}{\mathop{\lim }}\,\,\left( \sin x-x\cos x-x\tan x+2\cos x-\left. \frac{\sin x}{x} \right) \right.\] \[=0-0-0+2-1=1\].
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