1的无穷次方求极限 1的无穷次方型求极限，怎么做
1\u7684\u65e0\u7a77\u6b21\u65b9\u6781\u9650\u8bc1\u660e\uff1a
imf\uff08x\uff09\uff3eg\uff08x\uff09
\uff1dlime\uff3e\uff3bIn\uff08f\uff08x\uff09\uff3eg\uff08x\uff09\uff09\uff3d
\uff1dlime\uff3e\uff3bg\uff08x\uff09Inf\uff08x\uff09\uff3d
\uff1de\uff3e\uff3blim\uff3bg\uff08x\uff09Inf\uff08x\uff09\uff3d\uff3d
\u77e5\u9053imf\uff08x\uff09\uff3eg\uff08x\uff09\u662f\u5173\u4e8ex\u76841\u7684\u65e0\u7a77\u6b21\u65b9\u7c7b\u578b\u7684\u6781\u9650
\u6240\u4ee5f(x)->1 ,g(x)->\u221e
\u6240\u4ee5Inf(x)->0
\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u5f53t->0\u65f6,e^t-1 -> t
\u6211\u4eec\u4ee4t=Inf(x),\u5219e^Inf(x)-1 -> Inf(x)
\u6240\u4ee5Inf\uff08x\uff09\u4e0ee\uff3eInf\uff08x\uff09\uff0d1\uff08\u5373f\uff08x\uff09\uff0d1\uff09\u4e3a\u7b49\u4ef7\u65e0\u7a77\u5c0f
\u6240\u4ee5\uff0c
imf\uff08x\uff09\uff3eg\uff08x\uff09
\uff1de\uff3e\uff3blim\uff3bg\uff08x\uff09Inf\uff08x\uff09\uff3d\uff3d
\uff1de\uff3e\uff3blimg\uff08x\uff09\uff3bf\uff08x\uff09\uff0d1\uff3d\uff3d
\u6269\u5c55\u8d44\u6599
\u5229\u7528\u51fd\u6570\u6781\u9650\u7684\u56db\u5219\u8fd0\u7b97\u6cd5\u5219\u6765\u6c42\u6781\u9650\u3002
\uff1f\u5b9a\u74061\uff1f\uff1f\u2460\uff1f\uff1a\u82e5\u6781\u9650\uff1flim\uff1fx\u2192x\uff1f0f\uff08x\uff09\u548c\uff1flim\uff1fx\u2192x\uff1f0g\uff08x\uff09\u90fd\u5b58\u5728\uff0c\u5219\u51fd\u6570f\uff08x\uff09\u00b1g\uff08x\uff09\uff0cf\uff08x\uff09•g\uff08x\uff09
\u5f53x\u2192x\uff1f0\u65f6\u4e5f\u5b58\u5728\u4e14
\u2460\uff1flim\uff1fx\u2192x\uff1f0\uff3bf\uff08x\uff09\u00b1g\uff08x\uff09\uff3d\uff1d\uff1flim\uff1fx\u2192x\uff1f0f\uff08x\uff09\u00b1\uff1flim\uff1fx\u2192x\uff1f0g\uff08x\uff09
\u2461\uff1flim\uff1fx\u2192x\uff1f0\uff3bf\uff08x\uff09•g\uff08x\uff09\uff3d\uff1d\uff1flim\uff1fx\u2192x\uff1f0f\uff08x\uff09•\uff1flim\uff1fx\u2192x\uff1f0g\uff08x\uff09
\u53c8\u82e5\uff1flim\uff1fx\u2192x\uff1f0g\uff08x\uff09\u22600\uff0c\u5219f\uff08x\uff09g\uff08x\uff09\u5728x\u2192x\uff1f0\u65f6\u4e5f\u5b58\u5728\uff0c\u4e14\u6709
\uff1flim\uff1fx\u2192x\uff1f0f\uff08x\uff09g\uff08x\uff09\uff1d\uff1flim\uff1fx\u2192x\uff1f0f\uff08x\uff09\uff1flim\uff1fx\u2192x\uff1f0g\uff08x\uff09
\u5229\u7528\u6781\u9650\u7684\u56db\u5219\u8fd0\u7b97\u6cd5\u5219\u6c42\u6781\u9650\uff0c\u6761\u4ef6\u662f\u6bcf\u9879\u6216\u6bcf\u4e2a\u56e0\u5b50\u6781\u9650\u5b58\u5728\uff0c\u4e00\u822c\u6240\u7ed9\u7684\u53d8\u91cf\u90fd\u4e0d\u6ee1\u8db3\u8fd9\u4e2a\u6761\u4ef6\uff0c\u5982\u221e\u221e\u300100\u7b49\u60c5\u51b5\uff0c\u90fd\u4e0d\u80fd\u76f4\u63a5\u7528\u56db\u5219\u8fd0\u7b97\u6cd5\u5219\u3002
\u5fc5\u987b\u8981\u5bf9\u53d8\u91cf\u8fdb\u884c\u53d8\u5f62\uff0c\u8bbe\u6cd5\u6d88\u53bb\u5206\u5b50\u3001\u5206\u6bcd\u4e2d\u7684\u96f6\u56e0\u5b50\uff0c\u5728\u53d8\u5f62\u65f6\uff0c\u8981\u719f\u7ec3\u638c\u63e1\u996e\u56e0\u5f0f\u5206\u89e3\u3001\u6709\u7406\u5316\u8fd0\u7b97\u7b49\u6052\u7b49\u53d8\u5f62\u3002
\u4f8b1\uff1a\u6c42\uff1flim\uff1fx\u21922\uff1f\uff0dx\uff1f2\uff0d4x\uff0d2
\u89e3\uff1a\u539f\u5f0f\uff1d\uff1flim\uff1fx\u21922\uff1f\uff0d\uff08x\uff0d1\uff09\uff08x\uff0b2\uff09x\uff0d2\uff1d\uff1flim\uff1fx\u21922\uff1f\uff0d\uff08x\uff0b2\uff09\uff1d0
(1+1/n)^n, n趋向无穷大的时候就趋向e，所以要根据具体情况具体分析的。
图片上的原题中，指数 x → π/2，不是趋于无穷，直接代入得1
1^∞ 型不能直接等于1！(1+1/n)^n→e(n→∞)，
公式：N=e^(lnN), 然后 N^t=e^(t*lnN)，再讨论 t*lnN 的极限
无穷的0次方的极限不一定等于1，要利用对数恒等式x=e^(lnx)，将它化为零乘无穷的形式，最后化为0/0型，或者是无穷比无穷型求极限
无穷的0次方的极限不一定等于1，要利用对数恒等式x=e^(lnx)，将它化为零乘无穷的形式，最后化为0/0型，或者是无穷比无穷型求极限
无穷的0次方的极限不一定等于1，要利用对数恒等式x=e^(lnx)，将它化为零乘无穷的形式，最后化为0/0型，或者是无穷比无穷型求极限
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