Let f : [a, b] → R be a continuous function and suppose that N is a natural number. If ¤1,..., IN are real numbers in [a, b], prove that there is some xo in [a, b] such that f(x1) +·…·+ f(xN) ... f(ro) N
Let f : [a, b] → R be a continuous function and suppose that N is a natural number. If ¤1,..., IN are real numbers in [a, b], prove that there is some xo in [a, b] such that f(x1) +·…·+ f(xN) ... f(ro) N
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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![Let f : [a, b] → R be a continuous function and suppose that N is a natural number.
If ¤1,..., IN are real numbers in [a, b], prove that there is some xo in [a, b] such that
f(x1) +·…·+ f(xN)
...
f(ro)
N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9aa5134-abc6-4659-a50d-f4e106d6d7d8%2F72aaa86d-8109-444f-9271-dbe3f2b56a8a%2F7g82e1rg.png&w=3840&q=75)
Transcribed Image Text:Let f : [a, b] → R be a continuous function and suppose that N is a natural number.
If ¤1,..., IN are real numbers in [a, b], prove that there is some xo in [a, b] such that
f(x1) +·…·+ f(xN)
...
f(ro)
N
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