mathop {lim }limits_{theta to 0} frac{{4theta | vedclass

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Question

(B) આપણે જાણીએ છીએ કે $\mathop {\lim }\limits_{	heta 	o 0} \frac{{4	heta (	an 	heta - \sin 	heta )}}{{{{(1 - \cos 2	heta )}^2}}}$.$	an 	heta

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(B) આપણે જાણીએ છીએ કે $\mathop {\lim }\limits_{	heta 	o 0} \frac{{4	heta (	an 	heta - \sin 	heta )}}{{{{(1 - \cos 2	heta )}^2}}}$.$	an 	heta - \sin 	heta = \frac{\sin 	heta (1 - \cos 	heta )}{\cos 	heta }$ અને $1 - \cos 2	heta = 2\sin^2 	heta$ નો ઉપયોગ કરતા:$\mathop {\lim }\limits_{	heta 	o 0} \frac{{4	heta \sin 	heta (1 - \cos 	heta )}}{{\cos 	heta (2\sin^2 	heta )^2}} = \mathop {\lim }\limits_{	heta 	o 0} \frac{{2	heta \sin^2(	heta /2)}}{{\sin^3 	heta \cos 	heta }} = \frac{1}{2}$.

$\mathop {\lim }\limits_{\theta \to 0} \frac{{4\theta (\tan \theta - \sin \theta )}}{{{{(1 - \cos 2\theta )}^2}}}$ ની કિંમત શું છે?

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