mathop {lim }limits_{theta to 0} frac{{sin 3t | vedclass

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Question

(B) We need to evaluate the limit: $\mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 3	heta - \sin 	heta }}{{\sin 	heta }}$Using the formula $\sin

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) We need to evaluate the limit: $\mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 3	heta - \sin 	heta }}{{\sin 	heta }}$Using the formula $\sin 3	heta = 3\sin 	heta - 4\sin^3 	heta$:$= \mathop {\lim }\limits_{	heta 	o 0} \frac{{(3\sin 	heta - 4\sin^3 	heta) - \sin 	heta }}{{\sin 	heta }}$$= \mathop {\lim }\limits_{	heta 	o 0} \frac{{2\sin 	heta - 4\sin^3 	heta }}{{\sin 	heta }}$$= \mathop {\lim }\limits_{	heta 	o 0} (2 - 4\sin^2 	heta)$$= 2 - 4(0)^2 = 2$Alternatively,using the property $\mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin n	heta }}{{\sin 	heta }} = n$:$= \mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 3	heta }}{{\sin 	heta }} - \mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 	heta }}{{\sin 	heta }}$$= 3 - 1 = 2$

$\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin 3\theta - \sin \theta }}{{\sin \theta }} = $

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