Q:
Use the ε-δ definition of limit to prove that
l i m x^2 = 4
x-> 2
sol:
(1)
You must show that for each ε>0， there exists a δ>0 such that
|X^2-4| < ε whenever 0 < |X-2| < δ。
(2)
|X^2-4| = |X-2||X+2|。
(For all X in the interval (1,3), X+2 < 5 and thus |X+2|<5。
/* 我不懂為什麼要取1~3開區間，是可以隨便取嗎? */
/* 為何是取X+2 < 5，而不是 3<X+2 ? */
(3)So letting δ be the minimum of ε/5 and 1 , it follows that，
whenever 0<|X-2|<δ, you have
|X^2-4| = |X-2||X+2| < (ε/5)(5) = ε
/* the minimum ε/5 and 1 是哪裡來的?? */
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※ 編輯: pop10353 來自: 140.130.208.5 (09/24 09:31)