(1-cosX)/X当X趋于0时的极限是多少 求当x趋于0时，1-cosx除以x²的极限
Cos1/x \u5f53x\u8d8b\u4e8e0\u65f6\uff0c\u6781\u9650\u4e3a\u591a\u5c11\uff1f\u6574\u4f53\u7b80\u4ecb\uff1a
\u7814\u7a76\u51fd\u6570\u7684\u6781\u9650\u662f\u6574\u4e2a\u5fae\u79ef\u5206\u7684\u4e3b\u8981\u5185\u5bb9\uff0c\u4e8b\u5b9e\u4e0a\u6709\u5f88\u591a\u51fd\u6570\u5728\u67d0\u4e9b\u70b9\u4e8b\u4e0d\u8fde\u7eed\u7684\uff0c\u50cf\u8fd9\u4e2a\u51fd\u6570\u4e00\u6837\uff0c\u5728x->0\u7684\u65f6\u5019\u662f\u9707\u8361\u7684\u3002
\u4e3b\u8981\u65b9\u6cd5\uff1a\u5229\u7528\u5fae\u79ef\u5206\u4e2d\u6781\u9650\u5b58\u5728\u6027\u7406\u8bba
\u4e3b\u8981\u8fc7\u7a0b\uff1a
\u6ce8\u610f\u4e8b\u9879\uff1a
\u5224\u65ad\u4e00\u4e2a\u51fd\u6570\u5728\u67d0\u70b9\u7684\u6781\u9650\u5b58\u4e0d\u5b58\u5728\u5173\u952e\uff0c\u770b\u5728\u8fd9\u70b9\uff08\u65e0\u8bba\u4ee5\u4ec0\u4e48\u6837\u7684\u65b9\u5f0f\u8d8b\u8fd1\uff09\u6781\u9650\u662f\u5426\u4fdd\u5b58\u4e0d\u53d8\u3002
\u53c2\u8003\u6587\u732e\uff1a
\u590d\u65e6\u5927\u5b66\u300a\u6570\u5b66\u5206\u6790\u300b
\u5f53x~0\uff0c1-cosx~1/2x^2
\u6240\u4ee5\u7ed3\u679c\u4e3a1/2
当X趋于0时, cos x=1-(x^2)/2
原式=x/2
最后结果 0
lim(x→0)(1-cosx)/x=lim(x→0)(1-cosx)'/x'=lim(x→0)sinx=0
0
绛旓細涓嶈兘鐢ㄦ媺鏍兼湕鏃ヤ腑鍊煎畾鐞嗐傝繖棰樹笉鑳界敤鎷夋牸鏈楁棩涓煎畾鐞,鍥犱负鎷嗘垚[cos(sinx)-cosx]/(sinx-x)*(sinx-x)/(1-cosx)sinx涔嬪緦,鍒嗗埆璁＄畻姣忛」鏋侀檺.绗竴椤圭敤鎷夋牸鏈楁棩涓煎畾鐞嗗緱鏋侀檺鏄0,鑰岀浜岄」鐢ㄧ瓑浠锋棤绌峰皬鏇挎崲寰楁瀬闄愭槸鈭,鎵浠ヤ笉鑳藉埄鐢ㄧН鐨勬瀬闄愮瓑鏂兼瀬闄愮殑绉潵鎷嗗紑.
绛旓細澶归煎噯鍒欑殑璇,浣犺鍖栫畝涓嬪晩 1 - cosX = 2sin(X/2)^2 寰堟槑鏄2 sin(X/2)^2 > 0 鑰屼笖,鍦 [0,蟺/2] 涓,cos鏄皬浜1澶т簬0鐨,鏁, sin(X/2)^2 < sin(X/2)鎵浠 2sin(X/2)^2 < 2 sin(X/2)鍗 0 < 1 - cosX < 2 sin(X/2)2sin(X/2)瓒嬩簬0,鎵浠1 - cosX 瓒嬩簬0.....
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