Find the value of the limit $\lim _ { x \rightarrow 0 } \frac { \sin 6 t } { \sin 4 t }$ .
A)0
B)0.5
C)1
D)1.5
E)2
F)2.5
G)3
H)Does not exist

Question

Quizplus · Accepted Answer

The limit can be evaluated using the property that $\lim _ { x \rightarrow 0 } \frac { \sin x } { x } = 1$. Applying this property, we rewrite the given limit as $\lim _ { t \rightarrow 0 } \frac { 6 \sin 6 t / 6t } { 4 \sin 4 t / 4t }$. Since both $\sin 6t / 6t$ and $\sin 4t / 4t$ approach 1 as $t$ approaches 0, the limit simplifies to $6/4 = 1.5$.

Find the Value of the Limit lim⁡x→0sin⁡6tsin⁡4t\lim _ { x \rightarrow 0 } \frac { \sin 6 t } { \sin 4 t }limx→0​sin4tsin6t​

Find the Value of the Limit $\lim _ { x \rightarrow 0 } \frac { \sin 6 t } { \sin 4 t }$