Evaluate: mathop {lim }limits_{x to 0} frac{s | vedclass

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Question

(B) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$.$\mathop {\lim }\limits_{x 	o 0} \frac{\sin 4x}{\sin 2x} = \m

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$.$\mathop {\lim }\limits_{x 	o 0} \frac{\sin 4x}{\sin 2x} = \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin 4x}{4x} \cdot 4x \cdot \frac{1}{\frac{\sin 2x}{2x} \cdot 2x} ight)$$= \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin 4x}{4x} \cdot \frac{2x}{\sin 2x} \cdot \frac{4x}{2x} ight)$$= \left( \mathop {\lim }\limits_{4x 	o 0} \frac{\sin 4x}{4x} ight) \cdot \left( \mathop {\lim }\limits_{2x 	o 0} \frac{2x}{\sin 2x} ight) \cdot 2$$= 1 \cdot 1 \cdot 2 = 2$.

Evaluate: $\mathop {\lim }\limits_{x \to 0} \frac{\sin 4x}{\sin 2x}$

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