Let E = {p1, P2,, PN} be a finite subset of a closed interval [a, b), and g : [a, b] →R be a function such that g(r) = 0 for all r E [a, b] \ E. %3D (a) Using the function Xp(x) defined in Problem 2, show that one can express the function g as g(x) = g(p1)Xp (x) + g(p2)Xp2 (x) + - -+ g(PN)XpN (); (b) Show that g is Riemann integrable on [a, b), and find the value of g(x)dr.
Let E = {p1, P2,, PN} be a finite subset of a closed interval [a, b), and g : [a, b] →R be a function such that g(r) = 0 for all r E [a, b] \ E. %3D (a) Using the function Xp(x) defined in Problem 2, show that one can express the function g as g(x) = g(p1)Xp (x) + g(p2)Xp2 (x) + - -+ g(PN)XpN (); (b) Show that g is Riemann integrable on [a, b), and find the value of g(x)dr.
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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![Let E = {P1, P2, .. ,PN} be a finite subset of a closed interval [a, b], and g : [a, b] → R
be a function such that g(r) = 0 for all r E [a, b) \ E.
(a) Using the function Xp(x) defined in Problem 2, show that one can express the
function g as
g(r) = g(p1)Xp (*) + g(p2)Xp2 (r) + +g(PN)XpN ();
...
(b) Show that g is Riemann integrable on [a, b], and find the value of g(r)d.r.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7b644f44-345f-4275-b9b2-ffb00cbba336%2Fc02a4857-335d-4bdf-9c2e-daddfb716814%2Fde2rzsa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let E = {P1, P2, .. ,PN} be a finite subset of a closed interval [a, b], and g : [a, b] → R
be a function such that g(r) = 0 for all r E [a, b) \ E.
(a) Using the function Xp(x) defined in Problem 2, show that one can express the
function g as
g(r) = g(p1)Xp (*) + g(p2)Xp2 (r) + +g(PN)XpN ();
...
(b) Show that g is Riemann integrable on [a, b], and find the value of g(r)d.r.
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