为什么1-cosx=o(sinx)(x趋于0)
\u5f53x\u8d8b\u5411\u4e8e0\u65f6\uff0cx/sinx * (1+cosx)/cosx \u7684\u6781\u9650\u600e\u4e48\u6c42\uff1f\u6025\uff01\u5f53 x \u2192 0 \u65f6\uff0c
lim x/sinx * (1+cosx)/cosx
= lim x/sinx * lim[(1+cosx)/cosx]
= 1 * (2 / 1)
= 2
\u89e3\u7b54\u89c1\u56fe\uff1a
lim (x-->0) 2sin平方（x/2)/sinx
=lim (x-->0) x平方/(2x)
=0
绛旓細1-cosx=2sin骞虫柟锛坸/2)lim (x-->0) 2sin骞虫柟锛坸/2)/sinx =lim (x-->0) x骞虫柟/(2x)=0
绛旓細sinx=O(x) sin(2x)=O(x)寰楀嚭锛sin(1-cosx)=O(x)绉殑鍏崇郴锛歴in伪 = tan伪 脳 cos伪锛堝嵆sin伪 / cos伪 = tan伪 锛塩os伪 = cot伪 脳 sin伪 锛堝嵆cos伪 / sin伪 = cot伪锛塼an伪 = sin伪 脳 sec伪 (鍗 tan伪 / sin伪 = sec伪)...
绛旓細鎵浠(1-cosx)=o(2[sin(x/2)]^2)=o(x^2/2)
绛旓細鎴戠殑 璇佹槑sin(1-cosx)=o(x) 1涓洖绛 #鐑# 鐢熸椿涓湁鍝簺瀹炵敤鐨勫績鐞嗗鐭ヨ瘑?liufy_1985 2014-10-30 路 瓒呰繃78鐢ㄦ埛閲囩撼杩嘥A鐨勫洖绛 鐭ラ亾灏忔湁寤烘爲绛斾富 鍥炵瓟閲:131 閲囩撼鐜:100% 甯姪鐨勪汉:153涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏈洖绛旇鎻愰棶鑰呴噰绾 宸茶禐杩 宸茶俯杩< 浣犲杩欎釜鍥炵瓟鐨勮瘎浠锋槸?
绛旓細浜屽垎涔涓x鐨勫钩鏂 鐢ㄦ嘲鍕掑叕寮忓睍寮灏辫浜 f(x)=f(x0)+f'(x0)(x-x0)+f''(x0)(x-x0)^2/2!+f'''(x0)(x-x0)^3/3!+...杩欏氨鏄嘲鍕掑叕寮忥紝鐪佺暐鍙锋槸楂橀樁鏃犵┓灏忛噺锛屾湁鐨簹璇哄瀷浣欓」锛岀Н鍒嗗瀷浣欓」锛屾媺鏍兼湕鏃ュ瀷浣欓」绛 cosx=1-x^2/2+o(x^2)鍙互鐪 鏁板鍒嗘瀽 ...
绛旓細鈭 1-cosx = 1 - {1-2sin²(x/2)} = 2sin²(x/2)鍙 鈭 sin(x/2) 涓 (x/2) 鏄瓑浠锋棤绌峰皬 鈭 2sin²(x/2) 涓 2 * (x/2) ² 鍗 (x²)/2 鏄瓑浠锋棤绌峰皬 鈭 1-cosx鐨勬瀬闄愮瓑浜 (x²)/2 鐨勬瀬闄 ...
绛旓細sin鏂箈绛変簬1-cosx鏂广
绛旓細鐢辨嘲鍕掑叕寮忋俢os x =1-x^2/2!+x^4/4!-...(-1)^k*x^(2k)/(2k)!鎵浠1-cos x=x^2/2!-x^4/4!-...(-1)^k*x^(2k)/(2k)!鎵浠1-cosx~1/2x^2銆涓轰粈涔1-cosx=2sin^2x\2銆傜敱鍊嶈鍏紡cos2x=1-2(sinx)^2銆傚彲鐭2(sinx)^2=1-cos2x銆備护x=x/2銆傚湪楂樼瓑鏁板鐨勭悊璁虹爺绌...
绛旓細1-cosx绛変簬1/2(sinx/2)^2銆傚師寮=cos(2x)=(cosx)^2-(sinx)^2 =2(cosx)^2-1 =1-2(sinx)^2cos(2x)=1-2(sinx)^2 =1-2(sinx/2)^2 =1/2(sinx/2)^2 sin鍜宑os鐨勫叧绯绘槸锛歴in伪+cos伪=1锛泂inx=cos锛90-x锛夛紱tan伪=sin伪/cos伪锛泂in骞虫柟伪*cos骞虫柟伪=1銆俿in伪鏄寮...
绛旓細鐢辨嘲鍕掑叕寮忥細cos x =1-x^2/2!+x^4/4!-...(-1)^k*x^(2k)/(2k)!鎵浠1-cos x=x^2/2!-x^4/4!-...(-1)^k*x^(2k)/(2k)!鎵浠1-cosx~1/2x^2銆涓轰粈涔1-cosx=2sin^2x\2銆傜敱鍊嶈鍏紡cos2x=1-2(sinx)^2銆傚彲鐭2(sinx)^2=1-cos2x銆傚父鐢ㄧ殑璇卞鍏紡鏈変互涓嬪嚑缁勶細1銆...
