mathop {lim }limits_{theta to 0} frac{{5theta | vedclass

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Question

(A) To evaluate the limit $\mathop {\lim }\limits_{	heta 	o 0} \frac{5	heta \cos 	heta - 2\sin 	heta }{3	heta + 	an 	heta }$,divide both the n

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(A) To evaluate the limit $\mathop {\lim }\limits_{	heta 	o 0} \frac{5	heta \cos 	heta - 2\sin 	heta }{3	heta + 	an 	heta }$,divide both the numerator and the denominator by $	heta$:$\mathop {\lim }\limits_{	heta 	o 0} \frac{\frac{5	heta \cos 	heta - 2\sin 	heta}{	heta}}{\frac{3	heta + 	an 	heta}{	heta}} = \mathop {\lim }\limits_{	heta 	o 0} \frac{5\cos 	heta - 2\frac{\sin 	heta}{	heta}}{3 + \frac{	an 	heta}{	heta}}$Using the standard limits $\mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = 1$ and $\mathop {\lim }\limits_{	heta 	o 0} \frac{	an 	heta}{	heta} = 1$,and knowing $\cos(0) = 1$:$= \frac{5(1) - 2(1)}{3 + 1} = \frac{5 - 2}{4} = \frac{3}{4}$

$\mathop {\lim }\limits_{\theta \to 0} \frac{{5\theta \cos \theta - 2\sin \theta }}{{3\theta + \tan \theta }} = $

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