The number of solutions of 8 cos x = x will b | vedclass

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(B) To find the number of solutions of the equation $8 \cos x = x$,we can rewrite it as $\cos x = \frac{x}{8}$.This is equivalent to finding the numbe

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$4$

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(B) To find the number of solutions of the equation $8 \cos x = x$,we can rewrite it as $\cos x = \frac{x}{8}$.This is equivalent to finding the number of intersection points between the graphs of $y = \cos x$ and $y = \frac{x}{8}$.The graph of $y = \cos x$ oscillates between $-1$ and $1$ with a period of $2\pi \approx 6.28$.The line $y = \frac{x}{8}$ passes through the origin $(0, 0)$.For $x > 0$,the line $y = \frac{x}{8}$ reaches $y = 1$ at $x = 8$. Since $2\pi \approx 6.28$ and $4\pi \approx 12.56$,the line intersects the cosine curve at two points in the interval $(0, 8]$.For $x At $x = 0$,$\cos(0) = 1$ and $\frac{0}{8} = 0$,so there is no intersection at the origin.Counting the intersection points: two for $x > 0$ and two for $x < 0$,total $2 + 2 = 4$ solutions.

The number of solutions of $8 \cos x = x$ will be:

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