为什么对于lim1/cosx，当x从右边趋近于π/2时极限为无穷小，而从左边是无穷大呢？ 我有点乱，请帮忙一下~~ 当x趋于0时1/(1-cosx)是无穷大还是无穷小，为什么，...
\u4e3a\u4ec0\u4e48\u8fd9\u91cc\u4ece\u5de6\u8fb9\u8d8b\u8fd10\u662f\u65e0\u7a77\u5c0f\uff0c\u4ece\u53f3\u8fb9\u8d8b\u8fd10\u662f\u65e0\u7a77\u5927\u3002
\u5982\u56fe
limx-0,1-cosx-1-cos0=1-1=0
1-cosx\u4e3a\u65e0\u7a77\u5c0f\u91cf\uff0c
\u7b49\u4ef7\u4e8ex^2/2
limx-01/(1-cosx)=limx-01/x^2/2=2limx-01/x^2\u3002
\u6362\u5143\u6cd5\uff0c\u4ee4t=x^2,x-0,t-0^2=0,
2limt-0 1/t=2x\u65e0\u7a77=\u65e0\u7a77
\u6781\u9650\u503c\u4e3a\u65e0\u7a77\uff0c
x-0,x^2-0
x^2>=0,1/x^2>0\u3002
x^2>=0,1/x^2>0
x-0,x/=0,x^2>0,1/x^2>0
-\u65e0\u7a77<0,\u4e0d\u5c5e\u4e8e\uff080\uff0c+\u65e0\u7a77\uff09\u5185\uff0c\uff08\u820d\uff09\u3002
+\u65e0\u7a77>0,\u5728\uff080\uff0c+\u65e0\u7a77\uff09\u5185\uff0c\u6240\u4ee5\u53d6+\u65e0\u7a77\u3002
\u56e0\u4e3a\u65e0\u7a77\u5206\u4e3a\u65e0\u7a77\u5927\u548c\u65e0\u7a77\u5c0f\u4e24\u79cd\uff0c
\u65e0\u7a77\u5c0f<0,\u4e0d\u5c5e\u4e8e\uff080\uff0c+\u65e0\u7a77\uff09\uff08\u820d\uff09
\u4e24\u79cd\uff0c\u6392\u9664\u6389\u4e00\u79cd\u65e0\u7a77\u5c0f\uff0c\u90a3\u4e48\u5269\u4e0b\u7684\u4e00\u79cd\u65e0\u7a77\u5927\u80af\u5b9a\u662f\u6b63\u786e\u7b54\u6848\uff0c\u4e24\u79cd\uff0c\u6392\u9664\u63891\u79cd\uff0c\u5269\u4e0b\u7684\u4e00\u79cd\u80af\u5b9a\u662f\u6b63\u786e\u7b54\u6848\u3002
\u7b54\uff1a\u6781\u9650\u503c\u4e3a\u65e0\u7a77\u5927\uff0c\u65e0\u7a77\u5927\u662f\u4e0d\u5b58\u5728\uff0c\u6781\u9650\u503c\u4e0d\u5b58\u5728\u3002
x从右边趋近于π/2
即x>π/2， 此时cosx<0
即cosx趋于0-
所以1/cosx趋于负无穷大，而不是无穷小
x从左边趋近于π/2
即x<π/2， 此时cosx>0
即cosx趋于0+
所以1/cosx趋于正无穷大
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绛旓細lim(x鈫0)(x/sinx)绛変簬1銆傝В锛歭im(x鈫0)(x/sinx)=lim(x鈫0)(1/cosx) 锛堟礇蹇呰揪娉曞垯锛屽垎瀛愬垎姣嶅悓鏃舵眰瀵硷級=1/cos0 =1/1 =1 鍗砽im(x鈫0)x/sinx=1銆傚嵆lim(x鈫0)(x/sinx)绛変簬1銆傛礇蹇呰揪娉曞垯鏄湪涓瀹氭潯浠朵笅閫氳繃鍒嗗瓙鍒嗘瘝鍒嗗埆姹傚鍐嶆眰鏋侀檺鏉ョ‘瀹氭湭瀹氬紡鍊肩殑鏂规硶銆傞浂姣旈浂鍨 鑻ュ嚱鏁癴...
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