F(x) = log |sin x|,where x in (0, pi),is stri | vedclass

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(C) Given the function $f(x) = \log |\sin x|$ for $x \in (0, \pi)$.Since $x \in (0, \pi)$,$\sin x$ is always positive,so we can write $f(x) = \log(\si

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

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(C) Given the function $f(x) = \log |\sin x|$ for $x \in (0, \pi)$.Since $x \in (0, \pi)$,$\sin x$ is always positive,so we can write $f(x) = \log(\sin x)$.To find the intervals where the function is strictly increasing,we calculate the derivative $f'(x)$:$f'(x) = \frac{1}{\sin x} \cdot \cos x = \cot x$.For the function to be strictly increasing,we must have $f'(x) > 0$.Therefore,$\cot x > 0$.In the interval $(0, \pi)$,$\cot x$ is positive when $x \in \left(0, \frac{\pi}{2}\right)$.Thus,the function is strictly increasing on $\left(0, \frac{\pi}{2}\right)$.

$F(x) = \log |\sin x|$,where $x \in (0, \pi)$,is strictly increasing on

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