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Od. A function f: Rm→Rª is continuous if and only if for every x in Rm and ɛ>0, there exists 8>0 such that ||f(x)-f(y)||≤ɛ holds for all y with ||x-y||≤6. e. If f: Rm →R" is a function, if x in Rm, and if f(x)=limk→∞f(xk) holds whenever (x) in Rm is a sequence with limk→∞Xk=X, then f is continuous at x.

Od. A function f: Rm→Rª is continuous if and only if for every x in Rm and ɛ>0, there exists 8>0 such that ||f(x)-f(y)||≤ɛ holds for all y with ||x-y||≤6. e. If f: Rm →R" is a function, if x in Rm, and if f(x)=limk→∞f(xk) holds whenever (x) in Rm is a sequence with limk→∞Xk=X, then f is continuous at x.

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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Which of the following statements are true?

 

Od. A function f: Rm Rn is continuous if and only if for every x in Rm and >0, there exists 8>0 such that ||f(x)-f(y)||≤ɛ holds for all y with ||x-y||≤8. e. If f: Rm→R" is a function, if x in Rm, and if f(x)=limk→∞of(xk) holds whenever (xk) in Rm is a sequence with limk→∞oXk=X, then f is continuous at x.
Transcribed Image Text:Od. A function f: Rm Rn is continuous if and only if for every x in Rm and >0, there exists 8>0 such that ||f(x)-f(y)||≤ɛ holds for all y with ||x-y||≤8. e. If f: Rm→R" is a function, if x in Rm, and if f(x)=limk→∞of(xk) holds whenever (xk) in Rm is a sequence with limk→∞oXk=X, then f is continuous at x.
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