2. Suppose f is continuous on [a, b] and there exists a sequence {n} in [a, b] such that 0 ≤ f(xn) ≤ 1/1/2 n for all n E N. Prove that f(xo) = 0 for some xo € [a, b].

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 24E
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2. Suppose f is continuous on [a, b] and there exists a sequence {n} in [a, b] such that
0 ≤ f(xn) ≤ 1/1/2
n
for all n € N. Prove that f(x) = 0 for some xo € [a, b].
Transcribed Image Text:2. Suppose f is continuous on [a, b] and there exists a sequence {n} in [a, b] such that 0 ≤ f(xn) ≤ 1/1/2 n for all n € N. Prove that f(x) = 0 for some xo € [a, b].
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