麻烦各位数学高手帮一下，下面的几道题怎样用极限的准则证明啊？ 麻烦各位数学高手帮我解决一下这三道题。 不只要答案，还要详细...
\u6570\u5b66\u6781\u9650\u8bc1\u660e\u9898lim_(x->0){ln(1+x)/x}
=lim_(x->0){ln[(1+x)^(1/x)]}
=ln{lim_(x->0)(1+x)^(1/x)}=ln{e}=1.
lim_(x->0){(e^x-1)/x}
=lim_(x->0){(e^x-e^0)/(x-0)}
=f'(0)=1,
f(x)=e^x.
\u8fd9\u4e2a\u5e94\u8be5\u4e0d\u7b97\u7528\u5bfc\u6570\u5427\uff01
\u89e3\uff1a
10\u3001\u7531\u6761\u4ef6\u5f97\uff1a4\uff1d2a\uff0c
\u2234a\uff1d2\uff0c\u5373\u70b9M\u5750\u6807\u4e3a(2\uff0c2)\uff0c
\u8bbeP\u3001Q\u5750\u6807\u5206\u522b\u4e3a(t1^2/2\uff0ct1)\u3001(t2^2/2\uff0ct2)\uff0c\u76f4\u7ebfMP\u3001MQ\u3001PQ\u7684\u659c\u7387\u5206\u522b\u4e3ak1\u3001k2\u3001k\uff0c
\u2234k1\uff1d\uff0dk2\uff0c
\u800ck1\uff1d(t1\uff0d2)/(t1^2/2\uff0d2)\uff1d2(t1\uff0d2)/(t1^2\uff0d4)\uff1d1/(t1\uff0b2)\uff0c
k2\uff1d(t2\uff0d2)/(t2^2/2\uff0d2)\uff1d2(t2\uff0d2)/(t2^2\uff0d4)\uff1d1/(t2\uff0b2)\uff0c
\u22341/(t1\uff0b2)\uff1d\uff0d1/(t2\uff0b2)\uff0c
\u2234t1\uff0b2\uff1d\uff0d(t2\uff0b2)\uff0c
t1\uff0bt2\uff1d\uff0d4\uff0c
\u53c8k\uff1d(t1\uff0dt2)/(t1^2/2\uff0dt2^2/2)\uff1d2/(t1\uff0bt2)\uff0c
\u2234k\uff1d2/(\uff0d4)\uff1d\uff0d1/2\uff0c
\u2234\u9009A\uff1b
11\u3001\u8fde\u7ed3MN\uff0c\u5219|PM|\uff0d|PN|\u2264|MN|(\u5f53\u4e14\u4ec5\u5f53P\u3001M\u3001N\u4e09\u70b9\u5171\u7ebf\u65f6\u53d6\u201c\uff1d\u201d\u53f7)\uff0c
\u800cM\u3001N\u4e24\u70b9\u5206\u522b\u5728\u5706(x\uff0b4)^2\uff0by^2\uff1d4\u548c(x\uff0d4)^2\uff0by^2\uff1d1\u4e0a\uff0c
|MN|\u7684\u53d6\u503c\u8303\u56f4\u662f[5\uff0c11]\uff0c
\u2234|PM|\uff0d|PN|\u7684\u6700\u5927\u503c\u4e3a5\uff0c
\u2234\u9009A\uff1b
12\u3001\u8bbeF(x)\uff1df(x)/g(x)\uff0c
\u2234F(x)\uff1da^x\uff0c
\u5219F'(x)\uff1d[f'(x)g(x)\uff0df(x)g'(x)]/[g(x)]^2\uff0c
\u7531\u9898\u610f\u77e5F'(x)\uff1c0\uff0c
\u2234F(x)\u4e3a\u51cf\u51fd\u6570\uff0c0\uff1ca\uff1c1\uff0c
\u2234\u7531f(1)/g(1)\uff0bf(\uff0d1)/g(\uff0d1)\uff1d5/2\u5f97\uff1aa\uff0b1/a\uff1d5/2\uff0c
\u89e3\u5f97a\uff1d1/2\uff0c\u6216a\uff1d2(\u820d\u53bb)\uff0c
\u2234\u9009A
所以运用极限思想可以等于1
（2）这个与第一个的条件一样 n趋近无穷大 所以前面的很多项分子因为对与分母来说超级小 所以可以忽略 就看最后一项 将分母的n^2提出来可以开方后可以于分子约掉一个n 分数变为 n/根号（n^4+1） 1对于n来说很小（忽略） 加上前面合并可得1/3
（3）第三个他下面说X→0+ 这也是一个极限思想 可以把X先乘进去 分子与分母的X可以约掉 所以就等于1
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