Let Cr (R) denote the set of all real-valued functions defined on the real line that...

 

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Let Cr (R) denote the set of all real-valued functions defined on the real line that have a continuous nth derivative. Prove that C" (R) is a subspace of F(R, R). Let Cr (R) denote the set of all real-valued functions defined on the real line that have a continuous nth derivative. Prove that C" (R) is a subspace of F(R, R).