When we do improper integrals involving 1/∞ we always take granted that it is 0?
The question is the limit of lim n->∞ 1/n = 0, but 1/∞ is not.
When we do integrals, we neglect that fact completely, why?
Update:Andrew you aren't answering my question...
gintable, but when we take the limit to infinity of the summation we just found that it was a coincidence that it is the anti-derivative. The anti-derivative itself is not a limit
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In calculations a value which is extremely small can be treated as negligible.
1/∞ is technically not defined any more than 1/0 is. However it is a very small value.
As long as other values are significant then it is reasonable to treat 1/∞ as zero.
It would NOT be valid to take 1/∞ - 1/∞ = 0 however. It remains undefined because neither quantity is significant so they cannot give any valid defined result.
The limits need for researching the functions.To find out derivative need know the rule for it.It follow by integrals that we can figure out too. A lot of puzzles are for training only.In future it will be available count any integral themselves.
Because when we do integrals of any sort, the integration starts and ends are NOT the numbers themselves...but rather the LIMIT of the integration as we "paint closer and closer to the bounds". In otherwords, the "limits" of integration are exactly that...they are LIMITS. The integral itself is a limit.