数学：求下面图片上的极限，要详细过程，咋写？ 高等数学极限求解，要详细过程！
\u6570\u5b66\uff1a\u4e0b\u9762\u56fe\u7247\u4e2d\u7684\u6570\u5b66\u9898\u600e\u4e48\u6c42\u89e3(\u8be6\u7ec6\u8fc7\u7a0b)\uff1f\u7b54\u6848\u4e3a2016\uff0c\u8be6\u7ec6\u8fc7\u7a0b\u5982\u56fe\u8bf7\u53c2\u8003\u3002
\u9996\u5148\u4f60\u5f97\u77e5\u9053lim(1+1/n)^n=e n->\u65e0\u7a77\uff0c\u76f8\u5bf9\u5e94\u5c31\u662flim(1+x)^(1/x)=e x->0 \u3002
\u5f53n->\u65e0\u7a77\u7684\u65f6\u5019 ln(1+1/n)~1/n \u6240\u4ee5
(1+1/n)^n
=exp{n*ln(1+1/n)}
=exp{n*1/n}
=exp(1)
e
\u6240\u4ee51\u7684\u65e0\u7a77\u6b21\u65b9\u6709\u5982\u6b64\u7b80\u4fbf\u7b97\u6cd5\uff1af(x)^g(x) \u5176\u4e2df->1,g->\u65e0\u7a77 \u5f53x->0
f(x)^g(x)
=exp{ g(x) * (f(x)-1) }
\u6240\u4ee5\u4f60\u8fd9\u9898\u7684\u6781\u9650=exp{ 1/x * [(a^x+b^x)/2-1] }
=exp{ 0.5 * [(a^x-1)/x+(b^x-1)/x] }
(a^x-1)/x=lna x->0 L'Hospital\u6cd5\u5219
\u6781\u9650=exp{ 0.5 * (lna+lnb) } = \u6839\u53f7(ab)
用分子分母同时除以n就解决了——
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绛旓細))锝1/n+鈭(1+1/n²)锛1 浠=1/n瓒嬩簬闆 lim=lim(e^u/u锛1/u锛1)/(鈭(1+u²)+u锛1)=lim(e^u锛島锛1)(鈭(1+u²)锛島+1)/u(1+u²锛(u锛1)²)=lim(e^u锛島锛1)2/u(2u)绾︽帀2鍚庢礇蹇呰揪娉曞垯 =lim(e^u锛1)/2u =1/2 ...
