Let \( \mathrm{f}: \mathrm{R} \rightarrow(0,1) \) be a continuous f...

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Let \( \mathrm{f}: \mathrm{R} \rightarrow(0,1) \) be a continuous function. Then, which of the following function(s) has(have) the value zero at some point in the interval \( (0,1) \) ?
\( \mathrm{P} \)
(A) \( f(x)+\int_{0}^{\frac{\pi}{2}} f(t) \sin t d t \)
W
(B) \( x^{9}-f(x) \)
\( -(C) x-\int_{0}^{\frac{\pi}{2}-x} \mathrm{f}(\mathrm{t}) \cos \mathrm{t} d \mathrm{t} \)
(D) \( e^{x}-\int_{0}^{x} f(t) \sin t d t \)
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