Prove that the limit doesn't exist

[Chamika]

I am having a great trouble proving that the limit does not exist for the given piecewise function. I have tried to prove it using the method of contradiction. I want to make sure whether this approach is correct ? If you guys think there is any other alternative method better than this please tell me what that is ? A help would be much appreciated.

 

[blamocur]

I don't understand what you mean by 'piecewise' here. The function is not piecewise continuous, if that's what you mean.

Also, I tried and failed to understand the meaning of your approach Other readers might be able to figure it out, but my suggestion is to make your approach clearer.

 

[Steven G]

One limit is 0 while the other limit is b-a, which is not 0.
Now pick an appropriate epsilon.

 

[Dr.Peterson]

I don't understand what you mean by 'piecewise' here. The function is not piecewise continuous, if that's what you mean.

The phrase "piecewise function" is commonly used for what I prefer to call a "piecewise-defined function"; that is, it is defined separately on different pieces of the domain. It is not the same as "piecewise continuous".

 

[blamocur]

The phrase "piecewise function" is commonly used for what I prefer to call a "piecewise-defined function"; that is, it is defined separately on different pieces of the domain. It is not the same as "piecewise continuous".

I see.

By those definitions the function in the original post is not a piecewise function. I.e., your first links says "A piecewise function is a function that is defined on a sequence of intervals." (the emphasis is mine), and, similarly, the page pointed to by the second link says each "...sub-function applies to a different interval...".