Let the function \( \ln f(x) \) is defined where \( f(x) \) exists for \( x \geq 2 \& k \) is fi...

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Let the function \( \ln f(x) \) is defined where \( f(x) \) exists for \( x \geq 2 \& k \) is fixed positive real number, prove that if \( \frac{d}{d x}(x . f(x)) \leq-k f(x) \) then \( f(x) \leq A x^{-1-k} \) where \( A \) is independent of \( x \).
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