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July 24th, 2008, 07:42 AM   #1
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when should we evaluate left limit and right limit?

In some cases, we can just calculate a single limit and conclude that it is the limit without having to check the left-limit and right-limit separately. For example:



But in some cases, such conclusions may be wrong. For example.



This conclusion is wrong, as this is the right limit. If we calculate the left limit, we get:



Since, the left limit and the right limit are different, we should conclude that the limit does not exist. Shouldn't we have done a similar check for the first case too?

So, when should we just calculate one limit and be sure of its existence and when should we evaluate the right limit and left limit separately and see if they are equal?
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July 24th, 2008, 01:14 PM   #2
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Re: when should we evaluate left limit and right limit?

Quote:
Originally Posted by conjecture

So, when should we just calculate one limit and be sure of its existence and when should we evaluate the right limit and left limit separately and see if they are equal?
In theory you should always do left and right limits separately. However in many cases it will be obvious they are the same, so you don't have to do both.
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