MHB [ASK] Limit of Trigonometry Function

[Monoxdifly]

$$\lim_{x\to0}\frac{sin2x+sin6x+sin10x-sin18x}{3sinx-sin3x=}$$
A. 0
B. 45
C. 54
D. 192
E. 212

Either substituting or using L'Hopital gives $$\frac00$$. Is there any way to simplify it and make the result a real number?

 

[I like Serena]

We can repeat L'Hôpital until it's not $\frac 0 0$ any more.

 

[Monoxdifly]

Ah, I see. It's in the third derivative and the answer is $$\frac{4,608}{24}$$= 192, right?

 

[I like Serena]

Ah, I see. It's in the third derivative and the answer is $$\frac{4,608}{24}$$= 192, right?

Yep. (Nod)