posted by John on .
I am sorry. I am really struggling with limits. I am not sure of an answer for this problem either:
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.
I 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)