lim(x趋近0)x/cosx＝多少，请求步骤 lim X趋近于0 X/(1-cosX) =0 如何用夹逼准...

\u6c42\u6781\u9650 x \u8d8b\u4e8e0 lim(cosx)^1/(x^2) \u6c42\u6b65\u9aa4\uff01\uff01\uff01\uff01

\u5229\u7528\u5bf9\u6570\u6027\u8d28
(cosx)^(1/x^2)=e^[ln(cosx)^(1/x^2)]
=e^(1/x^2 * lncosx)
=e^(lncosx/x^2)
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\u4e00\u3001\u7b49\u4ef7\u65e0\u7a77\u5c0fln(1+x)\uff5ex,1-cosx\uff5e x^2/2
lim(lncosx/x^2)=lim ln[1+(cosx-1)]/x^2
=lim (cosx-1)/x^2
=lim (-x^2/2)/x^2
=-1/2
\u4e8c\u3001\u5229\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u5206\u5b50\u5206\u6bcd\u6c42\u5bfc\u53ca\u516c\u5f0flim sinx/x=1
lim(lncosx/x^2)=lim (-sinx/cosx)/2x
=lim (-1/2cosx)
=-1/2
\u6240\u4ee5\u539f\u5f0f=lim e^(lncosx/x^2)
=e^lim(lncosx/x^2)
=e^(-1/2)
\u6269\u5c55\u8d44\u6599\uff1a
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\u4ee4y=x/2, \u5219lim y=0\u3002
\u53ef\u4ee5\u8ba1\u7b97\u51fax/(1-cosx)=y/(sin y)^2
\u5f53lim y=0\u65f6\uff0cy\u548csin y\u662f\u540c\u9636\u65e0\u7a77\u5c0f\uff0c
\u6240\u4ee5lim x/(1-cosx)=lim 1/(sin y)=\u221e\u3002
\u9898\u76ee\u547d\u9898\u672c\u8eab\u662f\u9519\u7684\uff0c\u65e0\u4ece\u8bc1\u660e\u5b83\u7b49\u4e8e0\u3002

limx趋近于零x/cosx=0/1=0

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