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  • Choose the correct answer out of 4 options given against each Question 〖lim〗┬(x→0) ((tan⁡2x-x))/(3x-sin⁡x ) is

Choose the correct answer out of 4 options given against each Question

\mathop{\lim }_{x \rightarrow 0}\frac{ \left( \tan 2x-x \right) }{3x-\sin x}~  is 

A. 2
B. \frac{1}{2}
C. \frac{-1}{2}
D. \frac{1}{4}

Answers (1)

\\ \mathop{\lim }_{x \rightarrow 0}\frac{ \left( \tan 2x-x \right) }{3x-\sin x}=\mathop{\lim }_{x \rightarrow 0}\frac{ \left( \frac{\tan 2x}{x}-1 \right) }{ \left( 3-\frac{\sin x}{x} \right) }=\mathop{\lim }_{x \rightarrow 0}\frac{ \left( \frac{\text{2 tan}2x}{2x}-1 \right) }{ \left( 3-\frac{\sin x}{x} \right) }=\frac{2-1}{3-1}=\frac{1}{2} \\ \\

Hence, the answer is option B

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infoexpert21

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