mathop {lim }limits_{x to 0} frac{{sin ax}}{{ | vedclass

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Question

(A) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$.Given limit is $\mathop {\lim }\limits_{x 	o 0} \frac{\sin ax

Vedclass · Accepted Answer

$a/b$

Vedclass · Answer

(A) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$.Given limit is $\mathop {\lim }\limits_{x 	o 0} \frac{\sin ax}{\sin bx}$.Multiply and divide by $ax$ and $bx$:$= \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin ax}{ax} \cdot ax \cdot \frac{1}{\frac{\sin bx}{bx} \cdot bx} ight)$$= \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin ax}{ax} ight) \cdot \left( \frac{bx}{\sin bx} ight) \cdot \frac{ax}{bx}$$= 1 \cdot 1 \cdot \frac{a}{b} = \frac{a}{b}$.

$\mathop {\lim }\limits_{x \to 0} \frac{{\sin ax}}{{\sin bx}} = $

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