2.1 Show that a sequence of Riemann-Integrable functions f(x) converges uniformly toa Riemann-integrable function f(r).2.2 Define the sequence of functions {fn(x)} on [0, 1] by2n²r;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 limfn(x)dr.2.2.6 Under which condition(s) will limfa(z)dx = | lim fa(x)dx?n 00

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Answered: 2.1 Show that a sequence of…

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

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

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Question

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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