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teresatang
evaluate the limit of theta approaches zero of sin 3theta/ theta
\[\lim_{\theta \rightarrow 0}\sin \theta=\theta\] \[\lim_{\theta \rightarrow 0}\sin 3\theta=3\theta\] Can you finish it now?
To make life simpler, use \[\lim_{x \rightarrow 0} \frac{sinx}{x}=1\] \[\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{\theta}=\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{\theta}\times \frac{3}{3} =3\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{3\theta}=...\]
as theta approaches 0 the n 3theta also appoaches 0. now we know lim(sinx/x) approaches 1 as x approaches 0 hence lim ((sin(3theta))/theta) =3 *lim ((sin(3theta))/3theta) =3 as 3theta approaches 0.
Use the formula limx→0sinxx=1