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Vector Calculus

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Cthulhu:

--- Quote from: Ahmad on July 27, 2010, 09:33:43 pm ---Just as an aside in the way of counter-examples, there are limits that don't exist but for which if you approach along any polynomial path you get the same value!

--- End quote ---
I ran into this last semester. Confused the hell out of me.

QuantumJG:

--- Quote from: Ahmad on July 27, 2010, 09:33:43 pm ---Just as an aside in the way of counter-examples, there are limits that don't exist but for which if you approach along any polynomial path you get the same value!

--- End quote ---

Thanks I'll keep this in mind.

Ilovemathsmeth:
WOW I'd love to do this subject. I don't think Actuarial requires it though :(

tram:
ran into this question (or a very similar question) in umep....i don't get limits.... like, how do you know how you know which path you should approach the limit from to prove it dosen't exist? and if it's just a proof by contradiction, if the limit DOES exist, how do you prove it exists cos it's not like you can go though every single possibilty it and prove they ALL work.....

is there a thread explaining limits somewhere? soz to be all nooby >.<



--- Quote from: Ilovemathsmeth on July 28, 2010, 06:04:09 pm ---WOW I'd love to do this subject. I don't think Actuarial requires it though :(

--- End quote ---

Vector caculus is the subject they recommend you do in first semester for acturial if you've done umep. Thus it would be highly likely that some acturial studes people have done this subject.

kamil9876:
there are some techniques which account for every possible path.

For example if I want the limit as (x,y) approaches 0 of:


I bound it by:



and apply sandwhich theorem. (also to be rigorous you should mention that my inequality doesn't make sense when x=0, but when x=0 the function value is 0 anyway).

Read a precise definition of limits to remove any confusion.

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