Re: [證明]夾擠定理
※ 引述《eternal29 (29)》之銘言：
: show that lim xsin(1/x)=0 use the pinching theorem
: x→0
: 請板上的高手們幫個忙>"<
0 ≦ |sin(1/x)| ≦ 1
0 ≦ |(x)(sin(1/x))| ≦ |x|
lim 0 ≦ lim |(x)(sin(1/x))| ≦ lim |x|
x→0 x→0 x→0
Since lim 0 = 0 = lim |x| ,
x→0 x→0
by the pinching theorem , lim |(x)(sin(1/x))| = 0
x→0
lim (x)(sin(1/x)) = 0
x→0
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10/07 19:04, , 1F
10/07 19:04, 1F
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