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a. The function f: [0,1] → R given by f(x)=x¹/² is Lipschitz. b. The function f: [0,00) → R given by f(x)=1 is Lipschitz. c. The function f: [0,1] → R given by f(x)=x is Lipschitz. 1/2

a. The function f: [0,1] → R given by f(x)=x¹/² is Lipschitz. b. The function f: [0,00) → R given by f(x)=1 is Lipschitz. c. The function f: [0,1] → R given by f(x)=x is Lipschitz. 1/2

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?

 

b. a. The function f: [0,1] → R given by f(x)=x¹/² is Lipschitz. The function f: [0,00) → R given by f(x)=1 is Lipschitz. c. The function f: [0,1] → R given by f(x)=x is Lipschitz. Od. The function f: [0,00) → R given by f(x)=x¹/2 is Lipschitz. e. The function f: [0,00) → R given by f(x)=x² is Lipschitz. Of. The function f: [0,1] → R given by f(x)=1 is Lipschitz. g. The function f: [0,1] → R given by f(x)=x² is Lipschitz. h. The function f: [0,00) → R given by f(x)=x is Lipschitz.
Transcribed Image Text:b. a. The function f: [0,1] → R given by f(x)=x¹/² is Lipschitz. The function f: [0,00) → R given by f(x)=1 is Lipschitz. c. The function f: [0,1] → R given by f(x)=x is Lipschitz. Od. The function f: [0,00) → R given by f(x)=x¹/2 is Lipschitz. e. The function f: [0,00) → R given by f(x)=x² is Lipschitz. Of. The function f: [0,1] → R given by f(x)=1 is Lipschitz. g. The function f: [0,1] → R given by f(x)=x² is Lipschitz. h. The function f: [0,00) → R given by f(x)=x is Lipschitz.
Please note that every statement specifies a function and an interval, and it asks whether this particular function is Lipschitz (with some Lipschitz constant L=[0,00) that you do not have to specify) when considered on this particular interval.
Transcribed Image Text:Please note that every statement specifies a function and an interval, and it asks whether this particular function is Lipschitz (with some Lipschitz constant L=[0,00) that you do not have to specify) when considered on this particular interval.
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