Meesam T.

asked • 5d

How do we know?

There are some limits when evaluated give 0/0 ,∞/∞ or some other undefined thing yet if we solve it in a particular way there does exist a limit.But some simply can't be evaluated and are always undefined as given in the solutions at the back of the book.How do we know that those "undefined" limits according to the book are really undefined and can't be solved in some particular way?Like is there some rule for it?

1 Expert Answer

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Meesam T.

Thanks for your answer.Well that does make more sense.
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5d

Dayv O.

tutor
let me understand, then 1/x has some limit defined as long as x is not equal to zero but approaches zero? I think it is undefined.
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5d

Andrew F.

tutor
Dayv O. I find it more helpful to say limits exist or do not exist-- I would say the limit of 1/x exists for all non- zero numbers. If you prefer to say that when the value of a limit does not exist, then the limit is undefined, I do not object. I worry that this might create confusion-- can you say why you prefer to stress undefined?
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4d

Dayv O.

tutor
a matter of semantics is not my concern. Since the derivative is an example of 0/0 case (that is limit numerator and denominator are each zero as "h" approaches zero) and it is resolved with removable discontinuity I might have began my answer there. Meesam seems better informed so upvote job.
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4d

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