分子是根号下1-cos(X^2),注意是自变量x的平方,分母是1-cosX,X趋于0时的极限?
可根据导数的定义得x趋于0,[1-cos(x^2)]/(1-cosx)的极限
=[cos0^2-cos(x^2)]/(cos0-cosx)的极限
=x{[cos0^2-cos(x^2)]/(0^2-x^2)}除以
[(cos0-cosx)/(0-x)] 的极限
=x乘以cos(x^2)的导数/cosx的数 的极限
=x*[-2sin(x^2)}/(-sinx) 的极限
=2sin(x^2)*[x/sinx] 的极限
=2sin(x^2)*[(x-0)/(sinx-sin0)] 的极限
=2sin(x^2)*[1/(sinx的导数)] 的极限
=2sin(x^2)*(1/cosx) 的极限
=2sin(0^2)*(1/cos0)=0
绛旓細鏈鏈夎銆傛湰棰樼殑x蹇呴』瓒嬪悜浜0+锛岀粨鏋滄墠鏄1锛涜嫢瓒嬪悜浜0-锛岀粨鏋滄槸-1銆傝В绛旇鍥撅細
绛旓細锛濓紞锛坸^3/2锛夛紙arccosx锛塣2锛嬶紙3/8锛塼^2cost锛嶏紙3/8锛夆埆costd锛坱^2锛夛紜锛1/8锛塼^2cos3t 锛嶏紙1/8锛夆埆cos3td锛坱^2锛夛紳锛嶏紙x^3/2锛夛紙arccosx锛塣2锛嬶紙3/8锛墄锛坅rccosx锛塣2 锛嬶紙1/8锛夛蓟cos3锛坅rccosx锛夛冀锛坅rccosx锛塣2锛嶏紙3/4锛夆埆tcostdt锛嶏紙1/4锛夆埆tcos3tdt 锛濓紙...
绛旓細鍦ㄨ繖閲屽氨鏄妸x²锛媦²鐪嬫垚涓涓暣浣 鑰寈²锛媦²姝ゆ椂瓒嬩簬0 璁颁綇鍩烘湰鐨勭瓑浠锋棤绌峰皬1-cost绛変环浜0.5t²濡傛灉涓嶈寰楋紝鑷繁姹備釜鏋侀檺 limt瓒嬩簬0(1-cost)/0.5t² 娲涘繀杈炬硶鍒鍒嗗瓙鍒嗘瘝鍚屾椂姹傚 =limt瓒嬩簬0 sint /t=1 ...
绛旓細鍙互鐢ㄧН鍒嗕唬鎹紝浠x=sect;璇︾粏璁＄畻缁撴灉璇风湅鍥
绛旓細x鈫0锛1-cosx~x^2/2 甯哥敤鏃犵┓灏忎唬鎹㈠叕寮忥細褰搙鈫0鏃 sinx~x tanx~x arcsinx~x arctanx~x 1-cosx~1/2x^2 a^x-1~xlna e^x-1~x ln(1+x)~x (1+Bx)^a-1~aBx [(1+x)^1/n]-1~1/nx loga(1+x)~x/lna 姹傛瀬闄愬熀鏈柟娉曟湁锛1銆佸垎寮忎腑锛鍒嗗瓙鍒嗘瘝鍚岄櫎浠ユ渶楂樻锛屽寲鏃犵┓澶...
绛旓細=limcosx^2+sinx^2+cosx^2sinx^2-cosx^4/{x^21+cosx(cos2x)^(1/2)} =lim sinx^2(1+2cosx^2)/{x^21+cosx(cos2x)^(1/2)} =limsinx^2/x^2*lim(1+2cosx^2)/1+cosx(cos2x)^(1/2)=1*lim(1+2cosx^2)/1+cosx(cos2x)^(1/2)x=0浠ｅ叆锛氬師寮=3/2 瑙ｉ瑕佺偣灏...
绛旓細鏂规硶涓嶅彧涓绉嶏紝鏈甯哥敤鐨勬槸鐢ㄦ礇蹇呰揪娉曞垯锛屽氨鏄鍒嗗瓙鍒嗘瘝鍚屾椂姹傚銆傚垎姣嶆眰瀵煎緱-tanx锛屽垎瀛愭眰瀵煎緱-sinx/3(涓夋鏍瑰彿(cosx)^2)锛岀害鍒嗗緱涓夋鏍瑰彿cosx/3锛屽綋x瓒嬩簬0鏃讹紝缁撴灉绛変簬1/3.杩樻湁涓绉嶆槸灏嗗垎姣嶇瓑闃舵浛鎹㈡垚cosx-1. 鐒跺悗鐢ㄧ珛鏂瑰樊鍏紡cosx-1=(涓夋鏍瑰彿cosx-1)(涓夋鏍瑰彿(cosx)^2+涓夋鏍瑰彿cosx...
绛旓細(1-cosx)= 1- 锛坈os²x/2-sin²x/2锛=1- cos²x/2+sin²x/2=2sin²x/2 绛変环鏃犵┓灏忎唬鎹=2*锛坸/2锛²=x²/2 鎵浠ュ師寮=x/鈭2 / x =1/鈭2 =鈭2/2 甯屾湜瀵逛綘鏈夊府鍔㎡(鈭鈭)O~...
绛旓細杩欎釜鏄瀬闄愮殑绛変环鍏紡锛屾潵婧愪簬娉板嫆鍏紡锛岄渶瑕佸鏋侀檺鐨勭悊璁烘湁浜嗚В鎵嶈兘鐞嗚В
绛旓細绛旀姝ｇ‘銆傜瓟妗堢殑褰㈠紡涓嶅悓搴旇涓昏鏄悗闈㈣繖涓鏁板嚱鏁扮殑涓嶅悓琛ㄧず锛鍒嗗瓙鍒嗘瘝鍚屼箻浠ュ垎姣嶁垰(1-x^2)+1锛屽寲绠涓嬶紝鏁翠釜绗簩椤瑰寲鎴愪簡ln[|x|/(鈭(1-x^2)+1)]銆傚垎閮ㄧН鍒嗘椂锛岀浜岄儴鍒嗙殑閭ｄ釜涓嶅畾绉垎锛屽鏋滄妸鏍瑰彿涓鐨剎^2鎻愬嚭鏉ワ紝鍙互鍖栨垚浠ヤ笅鍏紡鐨勫舰寮忥細鈭玠x/鈭(x^2-a^2)=ln|x+鈭(x^2-a^2...
