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  • Evaluate <img alt="\mathrm{ \lim _{x \rightarrow 0} \frac{\tan (2 x)-x}{3 x-\sin (x)}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%20%5Clim%20_%7Bx%20%5Crightarrow%200%7

Evaluate \mathrm{ \lim _{x \rightarrow 0} \frac{\tan (2 x)-x}{3 x-\sin (x)}}

Option: 1

\frac{1}{2}


Option: 2

\frac{2}{3}


Option: 3

0


Option: 4

\frac{2}{5}


Answers (1)

best_answer

\mathrm{\lim _{x \rightarrow 0} \frac{\tan 2 x-x}{3 x-\sin x} =\lim _{x \rightarrow 0} \frac{\frac{2 \sin 2 x}{2 x \cos 2 x}-1}{3-\frac{\sin x}{x}} }

\mathrm{ =\frac{2 \cdot \frac{1}{\cos 0}-1}{3-1} }

\mathrm{ =\frac{1}{2} . }

Hence option 1 is correct.


 

Posted by

Ajit Kumar Dubey

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