連續函數與函數的極限

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Posted by admin | Posted in 01 極限與連續 | Posted on 17-06-2016

本文介紹函數連續的定義與求極限的手法,

並強調了求極限不可盲目代值。

 

 

按這裡下載

你覺得連續函數與函數的極限寫得如何?

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Comments (6)

很棒!! 之前在讀的時候,不太明白"可去間斷點"的概念
原來因式分解裡也有點學問

我想問一下17頁的例題1.19,就是從第一步到第二步中兩邊同乘以x的絕對值,那位甚麼中間的x不須加絕對值呢?

並不是同乘以 |x| ,而是同乘以 x ,這樣才會得到原式 x\sin(x) 。而同乘以 x 為什麼會得到

-|x|\leq x\sin(x)\leq |x|

而不是

-x\leq x\sin(x)\leq x

這是因為當 x\to0 ,它可能正可能負,如果是負的那樣寫會有問題。

例如 x=-0.5 ,就會變成

-(-0.5)\leq(-0.5)\sin(0.5)\leq-0.5

這樣大小順序是有問題的。加絕對值的版本才能確保大小順序無誤。

謝謝您~

看了之後才意識到會有「無法取極限」的情況出現
取極限前要先注意函數的定義域ouo

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