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12. If a function f is continuous in [a, b] and c e ]a, b[ such that f (c) # 0, then there exists some 8> 0' such that f (x) has the same sign as flc) for all rs lc -8 c+ 8r

12. If a function f is continuous in [a, b] and c e ]a, b[ such that f (c) # 0, then there exists some 8> 0' such that f (x) has the same sign as flc) for all rs lc -8 c+ 8r

Advanced Engineering Mathematics
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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12. If a function f is continuous in [a, b] andce ]a, b[ such that f (c) + 0, then there exists some 8>0' such that f (x) has the same sign as f (c) for all x e ]c-8, c + 8[.
Transcribed Image Text:12. If a function f is continuous in [a, b] andce ]a, b[ such that f (c) + 0, then there exists some 8>0' such that f (x) has the same sign as f (c) for all x e ]c-8, c + 8[.
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