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2.1 Show that a sequence of Riemann-Integrable functions fn(r) converges uniformly to a Riemann-integrable function f(r).

2.1 Show that a sequence of Riemann-Integrable functions fn(r) converges uniformly to a Riemann-integrable function f(r).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 54E
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2.1 Show that a sequence of Riemann-Integrable functions f(x) converges uniformly to a Riemann-integrable function f(r). 2.2 Define the sequence of functions {fn(x)} on [0, 1] by 2n²r; Sn(x) = { 2n(1 - nx); < 0; 2.2.1 Sketch on the same axis the graphs of fi(r) to fa(x). 2.2.2 Find f(x) = lim f,(a). 2.2.3 Evaluate S(x)dr. 2.2.4 Evaluate f fn(x)dr. 2.2.5 Evaluate lim fn(x)dr. 2.2.6 Under which condition(s) will lim fa(z)dx = | lim fa(x)dx? n 00
Transcribed Image Text:2.1 Show that a sequence of Riemann-Integrable functions f(x) converges uniformly to a Riemann-integrable function f(r). 2.2 Define the sequence of functions {fn(x)} on [0, 1] by 2n²r; Sn(x) = { 2n(1 - nx); < 0; 2.2.1 Sketch on the same axis the graphs of fi(r) to fa(x). 2.2.2 Find f(x) = lim f,(a). 2.2.3 Evaluate S(x)dr. 2.2.4 Evaluate f fn(x)dr. 2.2.5 Evaluate lim fn(x)dr. 2.2.6 Under which condition(s) will lim fa(z)dx = | lim fa(x)dx? n 00
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