Suppose that f is continuous on [a.b] that f(x) 20 for all xE[a,b] and that f =0 1. Prove that f(x) = 0 for all x E[a,b]· 2. Can we drop the continuity of f assumption without altering the previous result ?
Suppose that f is continuous on [a.b] that f(x) 20 for all xE[a,b] and that f =0 1. Prove that f(x) = 0 for all x E[a,b]· 2. Can we drop the continuity of f assumption without altering the previous result ?
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 2
b.
Suppose that f is continuous on [a.b]; that f(x) > 0 for all x E[a,b] and that
f= 0
1. Prove that f(x) = 0 for all x E[a,b]•
2. Can we drop the continuity of f assumption without altering the previous result ?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4482bb9c-9552-48b3-bfb7-f7649c9ad7d2%2Fd9f958bc-e76e-489f-ac6a-d611cfbe07fd%2F5tikl44_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 2
b.
Suppose that f is continuous on [a.b]; that f(x) > 0 for all x E[a,b] and that
f= 0
1. Prove that f(x) = 0 for all x E[a,b]•
2. Can we drop the continuity of f assumption without altering the previous result ?
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