4. For a function f:D → R and a point xo in D, define A = {x in D x ≥ xo} and B: {x in D x ≤ xo). Prove that f: D → R is continuous at xo if and only if → R and f: B → R are continuous at xo. f: A =

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
O
Porces or
questions
for
93 # 314 lapa
(f: DR D = A UB; whare A=fXED |
1.
wwxxo
skowi
at Xo
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B = {XED / X EX
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А
f.
fEt flA A → IR & f= FB B¬R
at to
Is continuous
fiA R&f: B¬R
47
exercise
fx D¬R
I are both continuous
Transcribed Image Text:O Porces or questions for 93 # 314 lapa (f: DR D = A UB; whare A=fXED | 1. wwxxo skowi at Xo exclse-type ㅈ and Let X ED ultral B = {XED / X EX 3.1 в хо А f. fEt flA A → IR & f= FB B¬R at to Is continuous fiA R&f: B¬R 47 exercise fx D¬R I are both continuous
4. For a function f: D → R and a point xo in D, define A = {x in D|x ≥ xo} and
B = {x in D | x ≤ xo}. Prove that f: D → R is continuous at xo if and only if
f: A → R and f: BR are continuous at xo.
Transcribed Image Text:4. For a function f: D → R and a point xo in D, define A = {x in D|x ≥ xo} and B = {x in D | x ≤ xo}. Prove that f: D → R is continuous at xo if and only if f: A → R and f: BR are continuous at xo.
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