mathop {lim }limits_{x to 0} frac{{sin 3x + s | vedclass

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Question

(C) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{\sin 3x + \sin x}}{x}$.Using the property of limits,we can split the expression:$

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$4$

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(C) We are given the limit: $\mathop {\lim }\limits_{x 	o 0} \frac{{\sin 3x + \sin x}}{x}$.Using the property of limits,we can split the expression:$= \mathop {\lim }\limits_{x 	o 0} \frac{\sin 3x}{x} + \mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x}$.Multiply and divide the first term by $3$:$= \mathop {\lim }\limits_{x 	o 0} 3 \cdot \frac{\sin 3x}{3x} + \mathop {\lim }\limits_{x 	o 0} \frac{\sin x}{x}$.Using the standard limit $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$:$= 3(1) + 1 = 3 + 1 = 4$.

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin 3x + \sin x}}{x} = $

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