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Let C(R) denote the vector space of continuous real valued functions

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Let C(R) denote the vector space of continuous real-
valued functions defined on R. Let D be the subset of C(R)
that consists of the differentiable functions. Is D a
subspace of C(R)? Justify your answer.
Solution
Yes it is, we just need to check closure
under addition and scalar multiplication. that is, sum of any
two differentiable function is again a differentiable function
- TRUE and scalar multiple of any differentiable function is
differentiable function -TRUE Thus is is subspace.

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Let C(R) denote the vector space of continuous real valued functions defined on R. Let D be the subset of C(R) that consists of the differentiable functions. Is D a subspace of C(R)? Justify your answer. Solution Yes it is, we just need to check closure under addition and scalar multiplication. th ...
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