Given that f,(x) = (n+ 1)(n+2)(1 – x)x" and that f(x) =0 for x E[0,1] 1. Show that the limit lim fn(x) =f(x) for each x E[0,1]- 2. Determine whether or not fn(x)dx- | f(x)dx for each x E[0,1];
Given that f,(x) = (n+ 1)(n+2)(1 – x)x" and that f(x) =0 for x E[0,1] 1. Show that the limit lim fn(x) =f(x) for each x E[0,1]- 2. Determine whether or not fn(x)dx- | f(x)dx for each x E[0,1];
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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![QUESTION 5
Given that f,(x) = (n + 1)(n+2)(1 – x)x" and that f(x) =0 for x E[0,1]
1. Show that the limit lim fn(x) = f(x) for each x E[0,1]:
11
2. Determine whether or not
fn(x)dx-
for each xE[0,1]
f(x)dx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec3f6ebc-75cc-4681-b2b0-807a38196ed7%2F0963a487-b474-4d65-9188-afcd73f3d823%2Fwk3ont_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 5
Given that f,(x) = (n + 1)(n+2)(1 – x)x" and that f(x) =0 for x E[0,1]
1. Show that the limit lim fn(x) = f(x) for each x E[0,1]:
11
2. Determine whether or not
fn(x)dx-
for each xE[0,1]
f(x)dx
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