Proposition 4.6.10. Let f : R → R be defined by f(x) = +b where a andbare constants. Then f is = ax continuous at any point c in R.
Proposition 4.6.10. Let f : R → R be defined by f(x) = +b where a andbare constants. Then f is = ax continuous at any point c in R.
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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Transcribed Image Text:Proposition 4.6.10. Let f : R → R be defined by f(x) = ax + b where a and bare constants. Then f is
continuous at any point c in R.
Proof. Let c be an arbitrary point in R and (æn :n € N) a sequence in R with æn → c. By definition of
f, f(xn) =1 Now since æ, → cit also holds that aæ, + b → ac + b. But ac +b= 2 Hence
3-4, and by invoking Theorem 5. we see that f must be 6 at any point c in R.
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