求Lim(x趋向于0)x^2的极限 求极限lim(x^2+y^2)/(x+y) ，x趋近于0、y...
lim(1-cosx)/x^2(x\u8d8b\u4e8e0\uff09\u6c42\u6781\u9650\u3002lim(1-cosx)/x^2(x\u8d8b\u4e8e0\uff09=1/2\u3002
\u89e3\u7b54\u8fc7\u7a0b\u5982\u4e0b\uff1a
\u201c\u6781\u9650\u201d\u662f\u6570\u5b66\u4e2d\u7684\u5206\u652f\u2014\u2014\u5fae\u79ef\u5206\u7684\u57fa\u7840\u6982\u5ff5\uff0c\u5e7f\u4e49\u7684\u201c\u6781\u9650\u201d\u662f\u6307\u201c\u65e0\u9650\u9760\u8fd1\u800c\u6c38\u8fdc\u4e0d\u80fd\u5230\u8fbe\u201d\u7684\u610f\u601d\u3002\u6570\u5b66\u4e2d\u7684\u201c\u6781\u9650\u201d\u6307\uff1a\u67d0\u4e00\u4e2a\u51fd\u6570\u4e2d\u7684\u67d0\u4e00\u4e2a\u53d8\u91cf\uff0c\u6b64\u53d8\u91cf\u5728\u53d8\u5927\uff08\u6216\u8005\u53d8\u5c0f\uff09\u7684\u6c38\u8fdc\u53d8\u5316\u7684\u8fc7\u7a0b\u4e2d\u3002
\u9010\u6e10\u5411\u67d0\u4e00\u4e2a\u786e\u5b9a\u7684\u6570\u503cA\u4e0d\u65ad\u5730\u903c\u8fd1\u800c\u201c\u6c38\u8fdc\u4e0d\u80fd\u591f\u91cd\u5408\u5230A\u201d\uff08\u201c\u6c38\u8fdc\u4e0d\u80fd\u591f\u7b49\u4e8eA\uff0c\u4f46\u662f\u53d6\u7b49\u4e8eA\u2018\u5df2\u7ecf\u8db3\u591f\u53d6\u5f97\u9ad8\u7cbe\u5ea6\u8ba1\u7b97\u7ed3\u679c\uff09\u7684\u8fc7\u7a0b\u4e2d\uff0c\u6b64\u53d8\u91cf\u7684\u53d8\u5316\uff0c\u88ab\u4eba\u4e3a\u89c4\u5b9a\u4e3a\u201c\u6c38\u8fdc\u9760\u8fd1\u800c\u4e0d\u505c\u6b62\u201d\u3001\u5176\u6709\u4e00\u4e2a\u201c\u4e0d\u65ad\u5730\u6781\u4e3a\u9760\u8fd1A\u70b9\u7684\u8d8b\u52bf\u201d\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u8bbe{xn}\u4e3a\u4e00\u4e2a\u65e0\u7a77\u5b9e\u6570\u6570\u5217\u7684\u96c6\u5408\u3002\u5982\u679c\u5b58\u5728\u5b9e\u6570a\uff0c\u5bf9\u4e8e\u4efb\u610f\u6b63\u6570\u03b5 \uff08\u4e0d\u8bba\u5176\u591a\u4e48\u5c0f\uff09\uff0c\u90fd∃N>0\uff0c\u4f7f\u4e0d\u7b49\u5f0f|xn-a|<\u03b5\u5728n\u2208(N,+\u221e)\u4e0a\u6052\u6210\u7acb\uff0c\u90a3\u4e48\u5c31\u79f0\u5e38\u6570a\u662f\u6570\u5217{xn} \u7684\u6781\u9650\uff0c\u6216\u79f0\u6570\u5217{xn} \u6536\u655b\u4e8ea\u3002
\u5728\u8fd0\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u4e4b\u524d\uff0c\u9996\u5148\u8981\u5b8c\u6210\u4e24\u9879\u4efb\u52a1\uff1a\u4e00\u662f\u5206\u5b50\u5206\u6bcd\u7684\u6781\u9650\u662f\u5426\u90fd\u7b49\u4e8e\u96f6(\u6216\u8005\u65e0\u7a77\u5927)\uff1b\u4e8c\u662f\u5206\u5b50\u5206\u6bcd\u5728\u9650\u5b9a\u7684\u533a\u57df\u5185\u662f\u5426\u5206\u522b\u53ef\u5bfc\u3002
\u5982\u679c\u8fd9\u4e24\u4e2a\u6761\u4ef6\u90fd\u6ee1\u8db3\uff0c\u63a5\u7740\u6c42\u5bfc\u5e76\u5224\u65ad\u6c42\u5bfc\u4e4b\u540e\u7684\u6781\u9650\u662f\u5426\u5b58\u5728\uff1a\u5982\u679c\u5b58\u5728\uff0c\u76f4\u63a5\u5f97\u5230\u7b54\u6848\uff1b\u5982\u679c\u4e0d\u5b58\u5728\uff0c\u5219\u8bf4\u660e\u6b64\u79cd\u672a\u5b9a\u5f0f\u4e0d\u53ef\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u6765\u89e3\u51b3\uff1b\u5982\u679c\u4e0d\u786e\u5b9a\uff0c\u5373\u7ed3\u679c\u4ecd\u7136\u4e3a\u672a\u5b9a\u5f0f\uff0c\u518d\u5728\u9a8c\u8bc1\u7684\u57fa\u7840\u4e0a\u7ee7\u7eed\u4f7f\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u3002
\u6d1b\u5fc5\u8fbe\u6cd5\u5219\u662f\u6c42\u672a\u5b9a\u5f0f\u6781\u9650\u7684\u6709\u6548\u5de5\u5177\uff0c\u4f46\u662f\u5982\u679c\u4ec5\u7528\u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u5f80\u5f80\u8ba1\u7b97\u4f1a\u5341\u5206\u7e41\u7410\uff0c\u56e0\u6b64\u4e00\u5b9a\u8981\u4e0e\u5176\u4ed6\u65b9\u6cd5\u76f8\u7ed3\u5408\uff0c\u6bd4\u5982\u53ca\u65f6\u5c06\u975e\u96f6\u6781\u9650\u7684\u4e58\u79ef\u56e0\u5b50\u5206\u79bb\u51fa\u6765\u4ee5\u7b80\u5316\u8ba1\u7b97\u3001\u4e58\u79ef\u56e0\u5b50\u7528\u7b49\u4ef7\u91cf\u66ff\u6362\u7b49\u7b49\u3002
lim (x²+y²)/(x+y)\uff0c\u6781\u5750\u6807\u7b80\u5316
=lim r²/(rcos\u03b8+rsin\u03b8)
=lim r/(cos\u03b8+sin\u03b8)
=0
\u5f88\u9ad8\u5174\u80fd\u56de\u7b54\u60a8\u7684\u63d0\u95ee\uff0c\u60a8\u4e0d\u7528\u6dfb\u52a0\u4efb\u4f55\u8d22\u5bcc\uff0c\u53ea\u8981\u53ca\u65f6\u91c7\u7eb3\u5c31\u662f\u5bf9\u6211\u4eec\u6700\u597d\u7684\u56de\u62a5
\u3002\u82e5\u63d0\u95ee\u4eba\u8fd8\u6709\u4efb\u4f55\u4e0d\u61c2\u7684\u5730\u65b9\u53ef\u968f\u65f6\u8ffd\u95ee\uff0c\u6211\u4f1a\u5c3d\u91cf\u89e3\u7b54\uff0c\u795d\u60a8\u5b66\u4e1a\u8fdb\u6b65\uff0c\u8c22\u8c22\u3002
\u2606\u2312_\u2312\u2606 \u5982\u679c\u95ee\u9898\u89e3\u51b3\u540e\uff0c\u8bf7\u70b9\u51fb\u4e0b\u9762\u7684\u201c\u9009\u4e3a\u6ee1\u610f\u7b54\u6848\u201d
lim(x->0) x^2 = 0
lim(x->0) x^2 = 0
0............................................
绛旓細Lim(x瓒嬪悜浜0)x^2鐨勬瀬闄 涓 0
绛旓細0 鍒嗘瀽锛氫唬鍏ュ嵆鍙lim(x->0) x^2 =0
绛旓細limx瓒嬪悜浜0 锛1-cosx锛/x²鐨勭粨鏋滅瓑浜1/2銆傝В锛lim(x鈫0)(1-cosx)/(x^2) 锛堟礇蹇呰揪娉曞垯锛屽垎瀛愬垎姣嶅悓鏃舵眰瀵硷級=lim(x鈫0)sinx/(2x) 锛堟礇蹇呰揪娉曞垯锛屽垎瀛愬垎姣嶅悓鏃舵眰瀵硷級=lim(x鈫0)cosx/2 =1/2 鍗砽im(x鈫0)(1-cosx)/(x^2)鐨勬瀬闄愬肩瓑浜1/2銆
绛旓細姹備笅鏋侀檺锛屽綋x瓒嬪悜0鏃讹紝lim锛坸鏂癸級/x=0锛屾墍浠ワ紝x鏂规槸姣攛楂橀樁鐨勬棤绌峰皬銆傦紙鎵璋撻樁灏辨槸瀹冭秼浜0鐨閫熷害銆傝秼浜0閫熷害鐩稿瓒婂揩锛屽氨鏄浉瀵归珮闃讹級銆備竴鑸湴锛宖锛x锛鍜屻愩恎锛坸锛夈戠殑k娆℃柟銆戝晢鐨勬瀬闄愭槸涓涓笉涓闆剁殑甯告暟锛屽垯f锛坸锛夋槸g锛坸锛夌殑k闃舵棤绌峰皬锛屽綋k鍙1鏃讹紝瀹冧滑鏄悓闃舵棤绌峰皬閲忥紱鐗瑰埆鍦...
绛旓細璁＄畻杩囩▼濡備笅锛
绛旓細鍏跺疄鍙互璁ㄤ釜宸 lim[x->0] x^2cot x^2=lim[t->0] t/tan t锛坱=x^2锛=lim[t->0] 1/(1/cos^2 t)=1
绛旓細瀵筬(x) = x^2锛屽叾鍦 x = 0 鐨勫乏瀵兼暟 f'-(0) = lim(x鈫0-)[f(x) - f(0)]/x = lim(x鈫0-)(x^2 - 0)/x = lim(x鈫0-)x = 0锛屽悓娉曞彲姹傚彸瀵兼暟f'+(0) = 0锛屾湁 f'-(0) = f'+(0)锛岀煡f(x) = x^2 鍦 x = 0 鍙锛屼笖 f'(0) = 0銆傚g(x) = x...
绛旓細lim x鐨剎娆℃柟锛寈瓒嬪悜0锛屽睘浜庘0鐨0娆♀濆瀷鏈畾寮忋1銆侀鍏堝x鐨剎娆℃柟 鍙栧鏁帮紝涓 xlnx锛屽啀鍐欎负lnx/(1/x)銆2銆佸綋x瓒嬪悜0锛鎴戣涓哄簲璇 x瓒嬪悜0+锛夋椂锛宭nx/(1/x)鏄滄棤绌锋瘮鏃犵┓鈥濆瀷鏈畾寮忥紝鐢ㄦ礇蹇呰揪娉曞垯銆3銆佸鍒嗗瓙鍒嗘瘝鍒嗗埆姹傚鏁帮紝鏈鍚庡緱鍒 xlnx 鐨勬瀬闄愪负 0 銆4銆佹敞鎰忓埌xlnx鏄敱 x...
绛旓細1.=lim(x瓒嬪悜浜0)[1+tanx-(1+sinx)]/[x(ln(1+x)-x)([(1+tanx)寮鏍瑰彿]+[(1+sinx)寮鏍瑰彿)]=lim(x瓒嬪悜浜0)[tanx(1-cosx)]/[2x(ln(1+x)-x)]=lim(x瓒嬪悜浜0)[x^2/2]/[2(ln(1+x)-x)]=lim(x瓒嬪悜浜0)[2x]/[4(-x/(1+x))]=-1/2 2.y'=2/3[锛坸+1)^(-...
绛旓細lim(x鈫0+)(x^x)=lim(x鈫0+) e^ln(x^x)=lim(x鈫0+) e^(xlnx)=e^lim(x鈫0+) (xlnx)=e^0 =1 鏋侀檺鐨勬剰涔夛細涓鑸潵璇达紝N闅徫电殑鍙樺皬鑰屽彉澶э紝鍥犳甯告妸N鍐欎綔N(蔚)锛屼互寮鸿皟N瀵刮电殑鍙樺寲鑰屽彉鍖栫殑渚濊禆鎬с備絾杩欏苟涓嶆剰鍛崇潃N鏄敱蔚鍞竴纭畾鐨勶細锛堟瘮濡傝嫢n>N浣縷xn-a|<蔚鎴愮珛锛...
