LIMITS
Let f (x) be defined and single-valued for all values of x near x = x0 with the possible exception of
X= x0 itslef We say that the number l is the limit of f(x ( as x
approaches x0 and write
lim f(x) = l if for
any positive number _ (however small) we can find some
positive number _ (usually depending on _) such that |f(x)-I|< whenever 0 < |x _ x0| < . Insuch
case we also say that f(x) approaches l as x approaches x0 and write f(x ً) l as x x0.
In words, this means that we can make f (x) arbitrarily close to l by choosing x sufficiently close tox0
RIGHT- AND LEFT-HAND LIMITS
In the de?nition of limit no restriction was made as to how x should approach x0. It is sometimes
found convenient to restrict this approach. Considering x and x0as points on the real axis where x0is
?xed and x is moving, thenx can approachx0from the right or from the leftsWe indicate these
respective approaches by writing x x0 .
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .