sin2派根号n的平方加n的极限 帮忙解极限：limsin²π√n2+n （n...
sin\u6d3e\u6839\u53f7\u4e0bn\u7684\u5e73\u65b9+1 \u6c42\u6781\u9650 n\u8d8b\u4e8e\u65e0\u7a77\u89e3\uff1a
\u4e0d\u8981\u51cf\u4e8cn\u6d3e\uff0c\u524d\u9762\u63d0\u6b63\u8d1f\uff0c\u51cfn\u6d3e\u3002\u63d0\u51fa\u6d3e\uff0c\u628a\u6839\u53f7\u4e0bn\u65b9\u51cf\u4e00\u51cfn\u505a\u5206\u5b50\uff0c\u4e0a\u4e0b\u540c\u4e58\u6839\u53f7\u4e0bn\u65b9\u51cf\u4e00\u52a0n\uff0c\u5206\u5b50\u4e3a\u5e73\u65b9\u5dee\uff0c\u7b49\u4e8e\u4e00\u3002\u6574\u7406\u5f97\u5230\u5206\u5b50\u4e3a\u6d3e\uff0c\u5206\u6bcd\u4e3a\u6839\u53f7\u4e0bn\u65b9\u51cf\u4e00\u52a0n\uff0cn\u8d8b\u4e8e\u65e0\u7a77\u65f6\uff0c\u5206\u6bcd\u8d8b\u4e8e\u65e0\u7a77\uff0c\u5206\u5f0f\u8d8b\u4e8e0\u3002\u5f97\u5230\u6b63\u8d1fsin0\u7b49\u4e8e0\uff0c\u7ed3\u679c\u4e3a0\u3002
\u51e0\u4f55\u5b66
\u65e0\u9650\u7ef4\u7684\u7a7a\u95f4\u5e38\u7528\u5728\u51e0\u4f55\u5b66\u53ca\u62d3\u6251\u5b66\u4e2d\uff0c\u5c24\u5176\u662f\u5728\u5206\u7c7b\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662fEilenberg−MacLane\u7a7a\u95f4\u3002\u5e38\u89c1\u7684\u4f8b\u5b50\u5305\u62ec\u65e0\u9650\u7ef4\u7684\u590d\u5c04\u5f71\u7a7a\u95f4K(Z,2)\uff0c\u4ee5\u53ca\u65e0\u9650\u7ef4\u7684\u5b9e\u5c04\u5f71\u7a7a\u95f4K(Z/2Z,1)\u3002
\u5206\u5f62\u7684\u7ed3\u6784\u53ef\u4ee5\u91cd\u590d\u7684\u653e\u5927\uff0c\u5206\u5f62\u53ef\u4ee5\u65e0\u9650\u6b21\u7684\u653e\u5927\uff0c\u4f46\u4e0d\u4f1a\u53d8\u7684\u5706\u6ed1\uff0c\u800c\u4e14\u4ecd\u7ef4\u6301\u539f\u6709\u7684\u7ed3\u6784\uff0c\u5206\u5f62\u7684\u5468\u957f\u662f\u65e0\u9650\u7684\uff0c\u6709\u4e9b\u7684\u9762\u79ef\u65e0\u9650\uff0c\u4f46\u6709\u4e9b\u7684\u9762\u79ef\u5374\u662f\u6709\u9650\u3002\u50cf\u79d1\u8d6b\u66f2\u7ebf\u5c31\u662f\u6709\u65e0\u9650\u5468\u957f\u548c\u6709\u9650\u9762\u79ef\u7684\u4f8b\u5b50\u3002
\u6781\u9650\u4e3a1\u3002
\u56e0\u4e3asin\u03c0n\uff1d0\u6240\u4ee5\u53ef\u4ee5\u8fd9\u6837\u505a\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u8ba9\u540e\u9762\u7684\u6709\u7406\u5316\u4e00\u4e0b\uff0c\u4e0a\u4e0b\u540c\u9664n\u5373\u53ef\u5f97\u5230\u6781\u9650\u4e3a1\u3002
sin\u540e\u76842\u662f\u5e73\u65b9\uff0c\u63a5\u7740\u662f\u6d3e\u4e58\u4ee5\u6839\u53f7\u4e0bn\u7684\u5e73\u65b9\u52a0\u4e0an\u7684\u548c\uff1bn\u8d8b\u5411\u65e0\u7a77\u3002
\u6c42\u6781\u9650\u57fa\u672c\u65b9\u6cd5\u6709\uff1a
1\u3001\u5206\u5f0f\u4e2d\uff0c\u5206\u5b50\u5206\u6bcd\u540c\u9664\u4ee5\u6700\u9ad8\u6b21\uff0c\u5316\u65e0\u7a77\u5927\u4e3a\u65e0\u7a77\u5c0f\u8ba1\u7b97\uff0c\u65e0\u7a77\u5c0f\u76f4\u63a5\u4ee50\u4ee3\u5165\u3002
2\u3001\u65e0\u7a77\u5927\u6839\u5f0f\u51cf\u53bb\u65e0\u7a77\u5927\u6839\u5f0f\u65f6\uff0c\u5206\u5b50\u6709\u7406\u5316\u3002
3\u3001\u8fd0\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u4f46\u662f\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u7684\u8fd0\u7528\u6761\u4ef6\u662f\u5316\u6210\u65e0\u7a77\u5927\u6bd4\u65e0\u7a77\u5927\uff0c\u6216\u65e0\u7a77\u5c0f\u6bd4\u65e0\u7a77\u5c0f\uff0c\u5206\u5b50\u5206\u6bcd\u8fd8\u5fc5\u987b\u662f\u8fde\u7eed\u53ef\u5bfc\u51fd\u6570\u3002
简单分析一下，详情如图所示
lim(n→无穷)sin^2((√n^2+n)π)=lim(n→无穷)sin^2((√n^2+n)π-nπ)=lim(n→无穷)sin^2((n/(√n^2+n)+n)π)=sin^2(π/2)=1
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绛旓細鈭礱n= 鏍瑰彿 2 sin(n蟺/ 2 + 蟺 /4 )锛庘埓瀵瑰簲鐨勬暟鍒楃殑鍛ㄦ湡T= 2蟺 / (蟺 /2 )=4锛屽嵆鏁板垪{an}鏄懆鏈熶负4鐨勫懆鏈熸暟鍒楋紝鈭碨12=3S4锛屸埖an= 鏍瑰彿2 sin(n蟺/ 2 + 蟺/ 4 )锛屸埓a1= 鏍瑰彿2 sin(蟺 /2 + 蟺 /4 )= 鏍瑰彿 2 cos(蟺/ 4 )锛宎2= 鏍瑰彿 2 sin(蟺+ 蟺 /4 )=-...
