X趋于∞，求极限。 lime（1／x）（x趋于∞），求极限·。过程
\u6c42\u6781\u9650\u65f6x\u8d8b\u5411\u4e8e \u221e\u548cx\u8d8b\u5411\u4e8e-\u221e\u6709\u4ec0\u4e48\u533a\u522b?\u672c\u6765\u662f\u6709\u660e\u663e\u533a\u522b\u7684\uff0c\u4e16\u754c\u5404\u56fd\u7684\u60ef\u4f8b\u4e5f\u662f\u6709\u533a\u522b\u7684\u3002
.
1\u3001x \u8d8b\u5411\u4e8e +\u221e\uff0c\u7b80\u5199\u4e3a x \u2192 \u221e\u3002
\u6b63\u53f7 \u201c+\u201d \uff0c\u7701\u7565\u4e0d\u5199\u662f\u975e\u5e38\u6b63\u5e38\u7684\u3002
x \u2192 3\uff0c\u7edd\u4e0d\u4f1a\u7406\u89e3\u6210\uff1a x \u2192 3\uff0c\u4e5f\u5305\u62ec x \u2192 -3\u3002
x \u2192 3\uff0c\u4ec5\u4ec5\u53ea\u662f\u6307 x \u2192 +3\uff0c\u7edd\u4e0d\u5305\u62ec x \u2192 -3\u3002
.
2\u3001\u4f46\u662f\uff0c\u6211\u4eec\u7684\u6559\u5b66\uff0c\u6700\u8fd1\u4e00\u4e8c\u5341\u5e74\u5185\uff0c\u51fa\u73b0\u4e86\u53e6\u7c7b\u3002
\u4ed6\u4eec\u628a x \u2192 \u221e\uff0c\u8bf4\u6210\u662f\u65e2\u5305\u62ec x \u2192 +\u221e\uff0c\u53c8\u5305\u62ec x \u2192 -\u221e\u3002
\u66f4\u6709\u751a\u8005\uff0c\u628a x \u2192 +\u221e\uff0cx \u2192 -\u221e \u8bf4\u6210\u662f x \u2192 \u221e \u7684\u5de6\u53f3\u6781\u9650\uff01
.
3\u3001\u56fd\u9645\u6559\u5b66\uff0c\u5728\u7406\u8bba\u6027\u7684\u3001\u539f\u7406\u6027\u7684\u3001\u6587\u5b57\u6027\u7684\u53d9\u8ff0\u4e2d\uff0c
x approaches infinity \uff08x \u8d8b\u5411\u4e8e\u65e0\u7a77\u5927\uff09\uff0c\u786e\u5b9e\u662f\u901a\u79f0\u3002
\u4f46\u662f\u5728\u5199\u6cd5\u4e0a x \u2192 \u221e\uff0c\u5c31\u662f\u6307 x \u2192 +\u221e\u3002
\u8fd9\u4e00\u70b9\u5728\u6570\u5217\u7684\u6781\u9650\u4e0a\uff0cn \u2192 \u221e\uff0c\u5c31\u662f\u6307 n \u2192 \u221e\uff0c\u5e76\u65e0\u5f02\u8bae\u3002
\u5728\u51fd\u6570\u7684\u6781\u9650\u4e0a\uff0c\u56fd\u5185\u5c11\u6570\u6559\u5e08\u8bd5\u56fe\u6539\u53d8\u56fd\u9645\u60ef\u4f8b\uff0c\u7ed3\u679c\u5982\u4f55\uff0c
\u662f\u53d1\u804b\u632f\u8069\u3001\u62e8\u4e71\u53cd\u6b63\uff0c\u8fd8\u662f\u53e6\u8d77\u7089\u7076\u3001\u80e1\u6405\u86ee\u7f20\uff0c\u4e0d\u5f97\u800c\u77e5\u3002
\u5f53x\u21920+\u65f6\uff0c1/x= + \u221e,e^(1/x) = e^(+\u221e) = +\u221e
\u5f53x\u21920-\u65f6\uff08\u6b64\u65f6x\u4e3a\u8d1f\u6570\uff09\uff0c\u67091/x= - \u221e,\u7531y=e^x\u7684\u56fe\u50cf\u53ef\u77e5
lim e^x = 0 (x\u2192 - \u221e)
\u6240\u4ee5\u624d\u4f1a\u6709lim e^(1/x)= +\u221e \uff08x\u21920+\uff09
lim e^(1/x) = 0 \uff08x\u21920-\uff09
\u4e5f\u5c31\u662f\u8bf4 lim e^(1/x) \uff08x\u21920\uff09 \u662f\u4e0d\u5b58\u5728\u7684
=lim(³√(1-u²)-1)/(1-cosu)
=lim(1/3)(1-u²)^(-2/3)(-2u)/sinu
=-2/3
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