想知道为什么例2为什么lim. X趋向于1的f(x)等于lim1 X趋向于1,为什麼不是2分之
\u5f53x\u8d8b\u5411\u4e8e0\u65f6,lim1\u7b49\u4e8e\u591a\u5c11,lim1=1
\u5e38\u6570\u7684\u6781\u9650=\u672c\u8eab\u3002
1
\u7ed3\u679c\u662f\u4ec0\u4e48\uff0c\u8fd8\u6ca1\u6709\u60f3\u5230\u600e\u4e48\u6c42\uff0c\u4f46\u662f\u5f88\u660e\u663e\uff0c\u51e0\u4e4e\u6240\u6709\u7684\u7b54\u6848\u90fd\u6709\u95ee\u9898\u3002\u505a\u4e00\u4e2a\u5047\u8bbe
a=b=c\uff0c
\u90a3\u4e48lim(((a^x+b^x+c^x)/3)^\uff081/x\uff09)=a=b=c\uff0c
\u73b0\u5728\u6240\u6709\u7684\u7b54\u6848\u90fd\u4e0d\u7b26\u5408\u8fd9\u4e2a\u7ed3\u8bba\u3002
\u6309\u7167 \u201c\u5b66\u592b\u5b50 \u7f51\u53cb\u201d\u56de\u7b54\uff1a
=lime^[ln((a^x+b^x+c^x)/3)/x]
=e^lim[3/(a^x+b^x+c^x)\u00d7\uff08(a^x+b^x+c^x)/3)']
=e^lim[3/(a^x+b^x+c^x)\u00d7((a^xlna+b^xlnb+c^xlnc)/3)]
\u7136\u540ex=0\uff0c\u4ee3\u5165\uff1b
=e^((3/3)X((lna+lnb+lnc)/3))
=e^((lna+inb+lnc)/3)
=(abc)^(1/3)
\u53e6\u5916\uff1ae^((lna+inb+lnc)/3) \uff01=abc/(e^3)
\u6b64\u65f6\u6ee1\u8db3\u4ee5\u4e0a\u7279\u4f8b\u60c5\u51b5\uff01
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