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3. Let 2 be an open bounded domain in RN partitioned into 1 and N2 (see figure below). 225 Let fi and f2 be two functions in C'(N) such that fi(x) = f2(x) for all a Er and Sfi (x) if r E N, f(x) = %3D f2(x) if r E 2. Show that for any a = (a1, a2,...,aN) such that Ja = 1, %3D D° fi(x) if a € N1, D° f(x) = D° f2(x) if x € N2.

3. Let 2 be an open bounded domain in RN partitioned into 1 and N2 (see figure below). 225 Let fi and f2 be two functions in C'(N) such that fi(x) = f2(x) for all a Er and Sfi (x) if r E N, f(x) = %3D f2(x) if r E 2. Show that for any a = (a1, a2,...,aN) such that Ja = 1, %3D D° fi(x) if a € N1, D° f(x) = D° f2(x) if x € N2.

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 2 be an open bounded domain in RN partitioned into 21 and N2 (see figure below). Let fi and f2 be two functions in C(2) such that fi(x) = f2(x) for all a E I and %3D f(x) = { i(x) if z E NI, f2(x) if r E N2. f (x) = %3D Show that for any a = (a1, a2,..., aN) such that Ja = 1, JD° fi(x) if a E N1, Dº f(x) = D° f2(x) ifx ε Ω2.
Transcribed Image Text:3. Let 2 be an open bounded domain in RN partitioned into 21 and N2 (see figure below). Let fi and f2 be two functions in C(2) such that fi(x) = f2(x) for all a E I and %3D f(x) = { i(x) if z E NI, f2(x) if r E N2. f (x) = %3D Show that for any a = (a1, a2,..., aN) such that Ja = 1, JD° fi(x) if a E N1, Dº f(x) = D° f2(x) ifx ε Ω2.
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