Re: 極限的証明
※ 引述《kimdo (水中抽菸)》之銘言:
: lim x^2=4
: x→2
: 怎麼證明
for all ε > 0 ,
if 0 < |x-2| < √(4 + ε) - 2
then
|x^2 - 4| = |x+2||x-2|
= |x-2 + 4||x-2|
≦(|x-2| + 4)|x-2|
<(√(4 + ε) + 2)(√(4 + ε) - 2) = ε
so
lim x^2 = 4 by definitions of limit
x→2
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