Let f (x) be continuous on [0, π], and be derivable in (0, π). It is proved that there exists ξ ∈ (0, π) such that f '(ξ) sin ξ + 2F (ξ) cos ξ = 0

F (x) = f (x) (SiNx) ^ 2; f '(x) = f' (x) (SiNx) ^ 2 + F (x) (2sinxcosx); it is easy to know from the condition that f (x) is continuous on [0, π] and derivable on (0, π), then: there exists ξ ∈ (0, π) such that f '(ξ) sin ξ sin ξ + 2F (ξ) cos ξ sin ξ = 0; if sin ξ is not zero, then: there exists ξ ∈ (0, π) such that f' (ξ

Let f (x) be continuous on [0, π], and be derivable in (0, π). It is proved that there exists ξ ∈ (0, π) such that f '(ξ) sin ξ + 2F (ξ) cos ξ = 0

Let f (x) be continuous on [0, π], and be derivable in (0, π). It is proved that there exists ξ ∈ (0, π) such that f '(ξ) sin ξ + 2F (ξ) cos ξ = 0

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