Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

Thanks