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Thm 1.22. a- Let f be continuous at a, 1. If f (a) > k, then 3 8 > 0 such that: ]x - al < 8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: x- a| < 8 = f(x)< k b- Let f be continuous from the right at a, 1. If f (a) > k, then 3 8 > 0 such that: a k 2. If f (a) < k, then 3 8 > 0 such that: a < x< a+ 8 = f(x) k, then 3 8 > 0 such that: a – 8 < x < a = f(x) >k 2. If f (a) < k, then 3 8 > 0 such that: a -8

Thm 1.22. a- Let f be continuous at a, 1. If f (a) > k, then 3 8 > 0 such that: ]x - al < 8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: x- a| < 8 = f(x)< k b- Let f be continuous from the right at a, 1. If f (a) > k, then 3 8 > 0 such that: a k 2. If f (a) < k, then 3 8 > 0 such that: a < x< a+ 8 = f(x) k, then 3 8 > 0 such that: a – 8 < x < a = f(x) >k 2. If f (a) < k, then 3 8 > 0 such that: a -8

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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Thm 1.22. a- Let f be continuous at a, 1. If f (a) > k, then 3 8 > 0 such that: |x- al <8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: x- al < 8 = f(x) < k b- Let f be continuous from the right at a, 1. If f(a) > k, then 3 8 > 0 such that: a <x<a+ 8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: a<x<a+ & = f(x) <k c- Let f be continuous from the left at a 1. If f (a) > k, then 3 8 > 0 such that: a-8 <x< a = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: a – 8 < x < a = f(x) <k
Transcribed Image Text:Thm 1.22. a- Let f be continuous at a, 1. If f (a) > k, then 3 8 > 0 such that: |x- al <8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: x- al < 8 = f(x) < k b- Let f be continuous from the right at a, 1. If f(a) > k, then 3 8 > 0 such that: a <x<a+ 8 = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: a<x<a+ & = f(x) <k c- Let f be continuous from the left at a 1. If f (a) > k, then 3 8 > 0 such that: a-8 <x< a = f(x) > k 2. If f (a) < k, then 3 8 > 0 such that: a – 8 < x < a = f(x) <k
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