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3. Let Co denote the vector space of functions f: R R which have derivatives of all orders. 1 Let S: C → C*, defined by S(f) = f', and let T: C0 + c* be a linear transformation such that T(sin' r) = x², and T(cos r) = cos r. Find To S(sin a cos x) or prove why it is not possible to do so with the given information.

3. Let Co denote the vector space of functions f: R R which have derivatives of all orders. 1 Let S: C → C*, defined by S(f) = f', and let T: C0 + c* be a linear transformation such that T(sin' r) = x², and T(cos r) = cos r. Find To S(sin a cos x) or prove why it is not possible to do so with the given information.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. Let Co denote the vector space of functions f: R →R which have derivatives of all orders.' Let S: C → C, defined by S(f) = f', and let T: C* → C* be a linear transformation such that T(sin? r) = x?, and T(cos? r) = cos r. Find To S(sin r cos r) or prove why it is not possible to do so with the given information.
Transcribed Image Text:3. Let Co denote the vector space of functions f: R →R which have derivatives of all orders.' Let S: C → C, defined by S(f) = f', and let T: C* → C* be a linear transformation such that T(sin? r) = x?, and T(cos? r) = cos r. Find To S(sin r cos r) or prove why it is not possible to do so with the given information.
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