Expert: Ahmed Salami - 9/10/2004

Question
Hi.
I want to know what limit is and how a limit is calculated. Thank you. and please tell me where you are from if you like!


Answer
Hi M_p
Forgive me for the horrible delay.
Well, i'm not sure that i can tell you everything about limits in this manner.
A function is usually with a dependent and an independent variable say y and x. As x continues to approach a particular value, it is sometimes interesting to know the value that y approaches. For instance, what does y approach as x approaches 4 if y = 2x - 3? This is pretty simple because you just have to insert x = 4 to get your answer. So, y approaches 2(4)- 3 = 5 as x approaches 4. In notation, this is written as lim(x~4) [2x - 3]= 5.
Sound easy but at times the usual method doesn't work. Now for another one that is not so direct.
Find lim(x~2) [(x^2 - 4)/(x - 2)].
Inserting 2 directly results in 0/0 which is meaningless, so we need another technique. All we have to do here is simplify (x^2 - 4)/(x - 2) to give (x-2)(x+2)/(x-2) to get (x + 2). Inserting the value x = 2 now gives us 4.
Therefore,
lim(x~2) [(x^2 - 4)/(x - 2)] = 4
There are more advanced forms and techniques of evaluating limits(e.g limits at infinity) and you would do well by going through a good text for more information as well as the correct notations.

I hope these little bit would help in its own little way. Sorry about the delay once again.
Good luck.

Just for your curiosity, i'm from Nigeria.
Regards.