One root of the equation cos x - x + fra | vedclass

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Question

Let $\mathrm{f}(\mathrm{x})=\cos \mathrm{x}-\mathrm{x}+\frac{1}{2}$

${f(0)=1+\frac{1}{2}>0} $

${f\left(\frac{\pi}{2}\right)=0-\frac{\pi}{2}+\

Vedclass · Accepted Answer

$\left( {0,\frac{\pi }{2}} \right)$

Vedclass · Answer

Let $\mathrm{f}(\mathrm{x})=\cos \mathrm{x}-\mathrm{x}+\frac{1}{2}$

${f(0)=1+\frac{1}{2}>0} $

${f\left(\frac{\pi}{2}\right)=0-\frac{\pi}{2}+\frac{1}{2}=\frac{1-\pi}{2}<0}$

Therefore, one root lies in the interval $\left(0, \frac{\pi}{2}\right)$.

One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval

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