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OpenStudy (anonymous):

limit of (tan 2*x)/x when x gets close to zero

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OpenStudy (anonymous):

rewrite tan(2x) as sin(2x)/cos(2x) then you can substitute...

OpenStudy (anonymous):

Rewrite it in the form \[ \lim_{x \rightarrow 0} 2 \cdot \frac{\sin(2x)}{2x} \cdot \frac{1}{\cos(2x)} \]

OpenStudy (anonymous):

\[\lim_{x \rightarrow 0}\frac{ \tan 2x }{ x} = \lim_{x \rightarrow 0}\frac{\sin 2x }{ x\cdot \cos 2x }= \lim_{x \rightarrow 0}\frac{2\sin 2x }{ 2x\cdot \cos 2x }= \lim_{x \rightarrow 0}\frac{\sin 2x }{ x\cdot \cos 2x }= \lim_{x \rightarrow 0}\frac{\sin 2x }{ 2x }\cdot\frac{2 }{ \cos 2x }\]

OpenStudy (anonymous):

\[\lim_{x \rightarrow 0}\frac{ \sin 2x }{ 2x }\cdot \lim_{x \rightarrow 0}\frac{ 2 }{ \cos 2x } = \lim_{u \rightarrow 0}\frac{ \sin u }{ u }\cdot \lim_{x \rightarrow 0}\frac{ 2 }{ \cos 2x }=1\cdot \frac{ 2 }{ 1 }=2\]

OpenStudy (anonymous):

Thanks

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