The smallest positive root of the equation ta | vedclass

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(C) To find the roots of the equation $	an x - x = 0$,we look for the intersection points of the graphs $y = 	an x$ and $y = x$.At $x = 0$,both func

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$\left(\pi, \frac{3\pi}{2}\right)$

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(C) To find the roots of the equation $	an x - x = 0$,we look for the intersection points of the graphs $y = 	an x$ and $y = x$.At $x = 0$,both functions are zero,but we are looking for the smallest positive root.For $x \in (0, \frac{\pi}{2})$,$	an x > x$,so there is no root in this interval.For $x \in (\frac{\pi}{2}, \pi)$,$	an x$ is negative while $x$ is positive,so there is no root.For $x \in (\pi, \frac{3\pi}{2})$,the graph of $y = 	an x$ starts from $-\infty$ and increases to $+\infty$,while $y = x$ is a line with a positive slope. They intersect at a point in the interval $(\pi, \frac{3\pi}{2})$.Thus,the smallest positive root lies in the interval $(\pi, \frac{3\pi}{2})$.

The smallest positive root of the equation $\tan x - x = 0$ lies in the interval

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