Question

evaluate the limit of theta approaches zero of sin 3theta/ theta

Answer 1

\[\lim_{\theta \rightarrow 0}\sin \theta=\theta\]
\[\lim_{\theta \rightarrow 0}\sin 3\theta=3\theta\]
Can you finish it now?

Answer 2

To make life simpler, use \[\lim_{x \rightarrow 0} \frac{sinx}{x}=1\]
\[\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{\theta}=\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{\theta}\times \frac{3}{3} =3\lim_{\theta\rightarrow 0} \frac{sin (3\theta)}{3\theta}=...\]

Answer 3

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.

Answer 4

Use the formula
limx→0sinxx=1