1. If Jis any subinterval of [a, b] and if ø,(x) := 1 for x E J and 4,(x) := 0 elsewhere on [a, b], we say that 4, is an elementary step function on [a, b]. Show that every step function is a linear combination of elementary step functions. %3D

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. If Jis any subinterval of [a, b] and if º, (x) :=1 for x E J and 4,(x) := 0 elsewhere on [a, b], we
say that o, is an elementary step function on [a, b]. Show that every step function is a linear
combination of elementary step functions.
Transcribed Image Text:1. If Jis any subinterval of [a, b] and if º, (x) :=1 for x E J and 4,(x) := 0 elsewhere on [a, b], we say that o, is an elementary step function on [a, b]. Show that every step function is a linear combination of elementary step functions.
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