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Calculus and Beyond Homework Help
Is f(t,y)=e^{-t}y Lipschitz Continuous in y?
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[QUOTE="the_dane, post: 6143896, member: 517904"] This is not so much a "Homework" question I am just giving an example to ask about a [U]specific[/U] topic. [h2]Homework Statement [/h2] Is ##f(t,y)=e^{-t}y## Lipschitz continuous in ##y## [h2]Homework Equations[/h2] I don't really know what to put here. Here is the definitions: [URL]https://en.wikipedia.org/wiki/Lipschitz_continuity[/URL] [h2]The Attempt at a Solution[/h2] I have found out that I can determine whether a function is Lipschitz continuous by looking at it's derivative ##f_y = df/dy## and see if it is bounded. In my case ##f_y=e^{-t}## is bounded in ##(y,f_y)## plane but is NOT bounded in ##(t,f_y)## plane. My conclusion is that ##f(t,y)## Lipschitz continuous in ##y##, right? I don't see why it should matter if ##f_y## is not bounded in ##(t,f_y)## plane. Is statement correct? [/QUOTE]
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Is f(t,y)=e^{-t}y Lipschitz Continuous in y?
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