A function \( y=f(x) \) satisfying the differential
equation \( \frac{d y}{d x} \cdot \sin x-y \.... VIDEO
A function \( y=f(x) \) satisfying the differential
\( \mathrm{P} \)
equation \( \frac{d y}{d x} \cdot \sin x-y \cos x+\frac{\sin ^{2} x}{x^{2}}=0 \) is such that, \( y \rightarrow 0 \) as \( x \rightarrow \infty \), then the statement which is correct?
(1) \( \lim _{x \rightarrow 0} f(x)=1 \)
(2) \( \int_{0}^{\pi / 2} f(x) d x \) is less than \( \frac{\pi}{2} \)
(3) \( \int_{0}^{\pi / 2} f(x) d x \) is greater than unity
(4) \( f(x) \) is an odd function
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