mathop {lim }limits_{x to 0} frac{{2{{sin }^2 | vedclass

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Question

(C) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 	heta }}{	heta } = 1$. Given expression is $\mathop {\lim }\limits_{x 	o 0} \fr

Vedclass · Accepted Answer

$18$

Vedclass · Answer

(C) We know that $\mathop {\lim }\limits_{	heta 	o 0} \frac{{\sin 	heta }}{	heta } = 1$. Given expression is $\mathop {\lim }\limits_{x 	o 0} \frac{{2{{\sin }^2}3x}}{{{x^2}}}$. $= 2 	imes \mathop {\lim }\limits_{x 	o 0} \left( \frac{{\sin 3x}}{x} ight)^2$. $= 2 	imes \mathop {\lim }\limits_{x 	o 0} \left( 3 	imes \frac{{\sin 3x}}{{3x}} ight)^2$. $= 2 	imes 3^2 	imes \left( \mathop {\lim }\limits_{3x 	o 0} \frac{{\sin 3x}}{{3x}} ight)^2$. $= 2 	imes 9 	imes (1)^2 = 18$.

$\mathop {\lim }\limits_{x \to 0} \frac{{2{{\sin }^2}3x}}{{{x^2}}} = $

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