Find, to two decimal places, $\lim _{\theta \rightarrow 0} \frac{8 \sin (6 \theta)}{\theta}$

A)48.00
B)1.33
C)1
D)0
E)DNE

Question

Find, to two decimal places, $\lim _{\theta \rightarrow 0} \frac{8 \sin (6 \theta)}{\theta}$

A)48.00
B)1.33
C)1
D)0
E)DNE

Quizplus · Accepted Answer

The limit can be solved using the standard limit formula $\lim _{\theta \rightarrow 0} \frac{\sin(\theta)}{\theta} = 1$. By substituting $6\theta$ for $\theta$, the expression becomes $8 \cdot 6 \cdot \lim _{\theta \rightarrow 0} \frac{\sin(6\theta)}{6\theta} = 48$, since $\lim _{\theta \rightarrow 0} \frac{\sin(6\theta)}{6\theta} = 1$.

Find, to Two Decimal Places lim⁡θ→08sin⁡(6θ)θ\lim _{\theta \rightarrow 0} \frac{8 \sin (6 \theta)}{\theta}limθ→0​θ8sin(6θ)​

Find, to Two Decimal Places $\lim _{\theta \rightarrow 0} \frac{8 \sin (6 \theta)}{\theta}$