lim _{x rightarrow 0} frac{cos 7 x^{circ}-cos | vedclass

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Question

(C) We know that $x^{\circ} = \frac{\pi}{180} x 	ext{ radians}$.So,the limit becomes $\lim _{x ightarrow 0} \frac{\cos \left(\frac{7 \pi}{180} xi

Vedclass · Accepted Answer

$\frac{-\pi^2}{1440}$

Vedclass · Answer

(C) We know that $x^{\circ} = \frac{\pi}{180} x 	ext{ radians}$.So,the limit becomes $\lim _{x ightarrow 0} \frac{\cos \left(\frac{7 \pi}{180} xight)-\cos \left(\frac{2 \pi}{180} xight)}{x^2}$.Using the standard limit formula $\lim _{x ightarrow 0} \frac{\cos(ax) - \cos(bx)}{x^2} = \frac{b^2 - a^2}{2}$,where $a = \frac{7\pi}{180}$ and $b = \frac{2\pi}{180}$:$= \frac{(\frac{2\pi}{180})^2 - (\frac{7\pi}{180})^2}{2}$$= \frac{1}{2} \cdot \frac{\pi^2}{180^2} (2^2 - 7^2)$$= \frac{1}{2} \cdot \frac{\pi^2}{32400} (4 - 49)$$= \frac{1}{2} \cdot \frac{\pi^2}{32400} (-45)$$= \frac{-45 \pi^2}{64800} = \frac{-\pi^2}{1440}$.

$\lim _{x \rightarrow 0} \frac{\cos 7 x^{\circ}-\cos 2 x^{\circ}}{x^2}$ is

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