આપેલ લક્ષની કિંમત શોધો: mathop {lim }limits_{ | vedclass

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Question

(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{x 	o 0} \frac{\sin ax}{bx}$$x=0$ મુકતા,વિધેય $\frac{0}{0}$ સ્વરૂપ ધારણ કરે છે.આપણે જાણીએ છીએ કે $\mathop {\li

Vedclass · Accepted Answer

$\frac{a}{b}$

Vedclass · Answer

(A) આપેલ લક્ષ: $\mathop {\lim }\limits_{x 	o 0} \frac{\sin ax}{bx}$$x=0$ મુકતા,વિધેય $\frac{0}{0}$ સ્વરૂપ ધારણ કરે છે.આપણે જાણીએ છીએ કે $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$.$\mathop {\lim }\limits_{x 	o 0} \frac{\sin ax}{bx} = \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin ax}{ax} 	imes \frac{ax}{bx} ight)$$= \mathop {\lim }\limits_{x 	o 0} \left( \frac{\sin ax}{ax} ight) 	imes \frac{a}{b}$જ્યારે $x 	o 0$,ત્યારે $ax 	o 0$ થાય. તેથી:$= \frac{a}{b} 	imes \mathop {\lim }\limits_{ax 	o 0} \left( \frac{\sin ax}{ax} ight)$$= \frac{a}{b} 	imes 1 = \frac{a}{b}$

આપેલ લક્ષની કિંમત શોધો: $\mathop {\lim }\limits_{x \to 0} \frac{\sin ax}{bx}$

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