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(A) First,we evaluate $\ell$: $\ell = \lim_{	heta ightarrow 0} \frac{3 \sin 	heta - 4 \sin^3 	heta}{	heta} = \lim_{	heta ightarrow 0} \frac{\

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$x^2 - 5x + 6 = 0$

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(A) First,we evaluate $\ell$: $\ell = \lim_{	heta ightarrow 0} \frac{3 \sin 	heta - 4 \sin^3 	heta}{	heta} = \lim_{	heta ightarrow 0} \frac{\sin(3	heta)}{	heta} = \lim_{	heta ightarrow 0} 3 \left( \frac{\sin(3	heta)}{3	heta} ight) = 3(1) = 3$. Next,we evaluate $m$: $m = \lim_{	heta ightarrow 0} \frac{2 	an 	heta}{	heta(1 - 	an^2 	heta)} = \lim_{	heta ightarrow 0} \frac{	an(2	heta)}{	heta} = \lim_{	heta ightarrow 0} 2 \left( \frac{	an(2	heta)}{2	heta} ight) = 2(1) = 2$. The quadratic equation with roots $\ell = 3$ and $m = 2$ is given by $x^2 - (\ell + m)x + \ell m = 0$. $x^2 - (3 + 2)x + (3 	imes 2) = 0$ $x^2 - 5x + 6 = 0$.

The quadratic equation whose roots are $\ell = \lim_{\theta \rightarrow 0} \left( \frac{3 \sin \theta - 4 \sin^3 \theta}{\theta} \right)$ and $m = \lim_{\theta \rightarrow 0} \left( \frac{2 \tan \theta}{\theta(1 - \tan^2 \theta)} \right)$ is

Similar Questions

The quadratic equation whose roots are $l$ and $m$,where
$\begin{aligned}
& l=\lim _{\theta \rightarrow 0}\left(\frac{3 \sin \theta-4 \sin ^2 \theta}{\theta}\right), \\
& m=\lim _{\theta \rightarrow 0} \frac{2 \tan \theta}{\theta\left(1-\tan ^2 \theta\right)}, \text{ is}
\end{aligned}$

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