Question

Trig limits help, I know the answer is 1/6, but don't know how they got it.

Answer 1

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Answer 2

\[\lim_{\theta \rightarrow 0}\frac{ \sin \theta }{ 5 \theta+\tan \theta }\]
\[divide~ the~ numerator~ and~ denominator~ by~\theta \]
\[=\frac{ \lim_{\theta \rightarrow 0}\frac{ \sin \theta }{\theta } }{ \lim_{\theta \rightarrow0}\left( 5+\frac{ \tan \theta }{\theta } \right) }\]
\[=\frac{ 1 }{ 5+1 }=\frac{ 1 }{6 }\]

Answer 3

Thank you :D