mathop {lim }limits_{theta to 0} frac{{1 - co | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Using the trigonometric identity $1 - \cos 	heta = 2 \sin^2(	heta/2)$,the limit becomes:$\mathop {\lim }\limits_{	heta 	o 0} \frac{2 \sin^2(

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(C) Using the trigonometric identity $1 - \cos 	heta = 2 \sin^2(	heta/2)$,the limit becomes:$\mathop {\lim }\limits_{	heta 	o 0} \frac{2 \sin^2(	heta/2)}{	heta^2} = \mathop {\lim }\limits_{	heta 	o 0} \frac{2 \sin^2(	heta/2)}{4(	heta/2)^2} = \frac{2}{4} \mathop {\lim }\limits_{	heta 	o 0} \left( \frac{\sin(	heta/2)}{	heta/2} ight)^2 = \frac{1}{2} 	imes (1)^2 = \frac{1}{2}$.Alternatively,applying $L$-Hospital's rule:$\mathop {\lim }\limits_{	heta 	o 0} \frac{1 - \cos 	heta}{	heta^2} = \mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{2	heta} = \frac{1}{2} \mathop {\lim }\limits_{	heta 	o 0} \frac{\sin 	heta}{	heta} = \frac{1}{2} 	imes 1 = \frac{1}{2}$.

$\mathop {\lim }\limits_{\theta \to 0} \frac{{1 - \cos \theta }}{{{\theta ^2}}} = $

Similar Questions

If $\theta$ is a small and positive number,then which of the following is/are correct?

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

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{1+\cos 2 x}{\cot 3 x\left(3^{\sin 2 x}-1\right)}=$

The value of $\mathop {\lim }\limits_{x \to 0} {(\cos ax)^{\csc^2 bx}}$ is-

$\lim _{x \rightarrow 0} \frac{\sin ^{2}\left(\pi \cos ^{4} x\right)}{x^{4}}$ is equal to :

Vedclass Test Series

Exam Paper Generator

Online Exam Module