2.4. Let J and J be real valued functions defined on a subset of a linear space Y, and suppose that for some y, v e Y, SJ(y; v) and SJ(y; v) exist. If ce R, establish existence and equality as required for the following assertions: (a) d(cJ)(y; v) = dJ(y; cv) = côJ(y; v). (b) 8(J + J)(y; v) = dJ(y; v) + dJ(y; v). Assuming the existence of the variations involved, (c) is SJ(cy; v) = cdJ(y; v)? (d) is SJ(y + ỹ; v) = SJ(y; v) + SJ(ỹ; v)?
2.4. Let J and J be real valued functions defined on a subset of a linear space Y, and suppose that for some y, v e Y, SJ(y; v) and SJ(y; v) exist. If ce R, establish existence and equality as required for the following assertions: (a) d(cJ)(y; v) = dJ(y; cv) = côJ(y; v). (b) 8(J + J)(y; v) = dJ(y; v) + dJ(y; v). Assuming the existence of the variations involved, (c) is SJ(cy; v) = cdJ(y; v)? (d) is SJ(y + ỹ; v) = SJ(y; v) + SJ(ỹ; v)?
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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please help me with letters (b) and (d). thanks
Transcribed Image Text:2.4. Let J and J be real valued functions defined on a subset of a linear space Y, and
suppose that for some y, v e Y, SJ(y; v) and SJ(y; v) exist. If ce R, establish
existence and equality as required for the following assertions:
(а) 6(сJ(у; v) — ӧJ(у; с)
(b) 8(J + Ny; 0) — 6J(у, 0) + 8J(у; ).
Assuming the existence of the variations involved,
(c) is SJ(cy; v) = cdJ(y; v)?
(d) is SJ(y + ỹ; v) = 8J(y; v) + SJ(ỹ; v)?
côJ(y; v).
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