Let F be the space of real valued functions. Which of the following statements are always correct? I. The set { sin x, cosx} is linearly independent. II. The set {sin x, cos x, x} is linearly dependent. III. The set {e", e is linearly dependent. IV. The set {e", e", e"} is linearly independent.

Q: find F as a function of x and evaluate it at x = 0, x = π/4, and x = π/2.

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Q: 1, sin?x, cos?x

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Q: e*, cos x, sin x

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A: Case1: Whenfx=0 , then ∫abfxdx=0 is obvious.

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Q: Prove the following statement: For any function f : R" - R and any function g : R" R, let h: R" R be…

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A: He we will prove the given result.

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A: Introduction: There must be at least one "c" such that c∈(a,b) (or a&lt;c&lt;b) and f(c) = L. if…

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Q: f (x)dx = f(c)(b – a). a

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A: NOTE: Refresh your page if you can't see any equations. . take derivative

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A: Since the function g is continuous.So, limx→1-g(x)=g(1)limx→1-x2-mx=-212-m(1)=-2m=1+2m=3

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