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July 31, 2014

July 31, 2014

Posted by **John** on Saturday, September 18, 2010 at 7:21pm.

Show an example that the limit as x goes to a f(x) goes to [f(x)+g(x)] may exist even though neither the limit as x goes to a f(x) approaches f(x) or g(x) exist.

- Calculus -
**MathMate**, Saturday, September 18, 2010 at 8:46pmI have difficulties understanding the question exactly. Could you post the question as it is shown in the book? If there are italics font on certain expressions, put them between double quotes.

The limit of a function f(x) as x→a can exist even if f(x) does not exist. The conditions are that

both Lim x→a+ and Limx→a- must exist (i.e. not ±∞).

Also the two limits must be equal.

An example is f(x)=(x-1)(x+2)/(x-1)

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