lim（x趋于0）xcos1/x 等于多少 limx趋向于0xcos1/x=?
\u8ba1\u7b97lim(x\u8d8b\u54110)xcos1/x\u7684\u6781\u96500
lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5\uff08cos1/x\uff09
=lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5lim(x\u8d8b\u5411\u4e8e0)\uff08cos1/x\uff09
\u7531\u4e8elim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09=0\uff0c\u662f\u65e0\u7a77\u5c0f\u91cf\uff0c
\u800c|lim(x\u8d8b\u5411\u4e8e0)\uff08cos1/x\uff09|<=1,\u662f\u6709\u754c\u91cf\uff0c
\u6839\u636e\u65e0\u7a77\u5c0f\u91cf\u4e58\u4ee5\u6709\u754c\u91cf\u7b49\u4e8e\u65e0\u7a77\u5c0f\u91cf\uff0c\u77e5
lim(x\u8d8b\u5411\u4e8e0)\u65f6\uff08x\u7684\u5e73\u65b9\uff09\u4e58\u4ee5\uff08cos1/x\uff09=0
\u4e8b\u5b9e\u4e0a\uff0c\u5f53x\u8d8b\u8fd1\u4e8e\u96f6\u65f6\uff0ccos\uff081/x\uff09\u548csin\uff081/x\uff09\u90fd\u662f\u5728\u533a\u95f4[-1,1]
\u4e0a\u7684\u65e0\u7a77\u8df3\u53d8\u51fd\u6570\u3002
则cosx在[-1,1]震荡，即有界
x→0
所以lim(x→∞)xcos(1/x)=0
绛旓細0
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