求极限LIM(X趋向0）tanx-sinx/x3次方,
LIM(X趋向0）tanx-sinx/x3次方=lim(x->0)tanx(1-cosx)/x³
=lim(x->0)(x·x²/2)/x³
=1/2
绛旓細鍘熼锛姹傛瀬闄恖im鈹(x鈫0)銆(tanx-sinx)/x^3 銆楁垜鐨勭瓟妗 lim[x鈫0] (tanx-sinx)/x³=lim[x鈫0] (sinx/cosx-sinx)/x³=lim[x鈫0] (sinx-sinxcosx)/(x³cosx)=lim[x鈫0] sinx(1-cosx)/(x³cosx)=lim[x鈫0] sin³x(1...
绛旓細绠鍗璁＄畻涓涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細鍏蜂綋鍥炵瓟濡備笅锛lim(x瓒嬪悜浜0+锛墄^tanx =e^lim(x瓒嬪悜浜0+锛塴nx^tanx =e^lim(x瓒嬪悜浜0+锛塴nx*tanx =e^lim(x瓒嬪悜浜0+锛塴nx/cotx (鈭/鈭)=e^lim(x瓒嬪悜浜0+锛(1/x)/(-csc^2x)=e^lim(x瓒嬪悜浜0+锛-sinx =e^0 =1 鏋侀檺鍑芥暟鐨勬剰涔夛細鍦ㄥ尯闂(a-蔚锛宎+蔚)涔嬪鑷冲鍙湁N涓紙鏈夐檺涓...
绛旓細鏈変笁绉璁＄畻鏂规硶锛屽叿浣撳涓嬶細1銆佸彧瑕佷唬鍏ュ悗锛岃兘绠楀嚭涓涓叿浣撶殑鏁板硷紝灏卞彲浠ヤ唬鍏ワ紱2銆佽嫢浠ｅ叆鍚庯紝铏界劧寰椾笉鍒颁竴涓叿浣撶殑鏁板硷紝浣嗘槸鑳藉緱鍒版棤绌峰ぇ鐨勭粨璁猴紝灏卞啓涓娾鏋侀檺涓嶅瓨鍦ㄢ濓紝鏋侀檺鏄棤绌峰ぇ锛屾棤璁烘槸姝ｆ槸璐燂紝灏辨槸鏋侀檺涓嶅瓨鍦ㄣ傛瀬闄愪笉瀛樺湪锛屼篃鏄畾寮忋備篃灏辨槸鑳界珛鍒昏兘纭畾缁撴灉鐨勬瀬闄愬紡銆3銆佽嫢浠ｅ叆鍚庯紝寰楀埌...
绛旓細lim(x鈫0)[(鈭(0,x)tan²tdt)/ln(1+x³)] =lim(x鈫0) [d(鈭(0,x)tan²tdt)/dx]/[dln(1+x³)/dx]锛堟礇姣旇揪娉曞垯锛=lim(x鈫0){(tan²x)/[3x²/(1+x³)]}锛堚︹鈭(0,x)f(t)dt / dx = f(x)锛=lim(x鈫0)[(tan²x...
绛旓細瀵瑰垎瀛愬垎姣嶅垎鍒眰瀵兼湁锛歭im2x(tanx-x)/(tanx-sinx)=lim2x(tanx-x)/(1/2x^3)=lim4(tanx-x)/x^3 =lim4(tanx-x)/x^2=lim2(sec^2x-1)/x=2lim(tanx)^2/x=4limtanx*(secx)^2=0
绛旓細=lim(x鈫0)[2*(-sinx)/x]锛
绛旓細鑰冪爺棰橈紝鐔熸倝楹﹀厠鍔充鸡鍏紡锛屽彧闇瑕佷笁涓瓑鍙凤紝鍥剧墖鏈鍚庝竴琛屽彲鐣ヤ负涓涓瓑鍙凤紝璇风偣鍑昏緭鍏ュ浘鐗囨弿杩
绛旓細姹傛瀬闄恖im(x瓒嬪悜0) (tanx-x)/(x^2arctanx锛変娇鐢ㄦ棤绌峰皬绛夐噺浠ｆ崲锛屾垨鑰呮礇蹇呰揪娉曞垯锛屾垨鑰呬娇鐢ㄦ嘲鍕掑叕寮忔潵姹傝В 鍦▁瓒嬪悜0鏃讹紝鏈 tanx-x~ x^3/3 arctanx~x 甯﹀叆鍙煡锛 =lim x^3/3 /(x*x^2) =1/3
绛旓細鍒╃敤鏃犵┓灏忕殑绛変环浠ｆ崲娉姹俵imtan3x/sin2x(x瓒嬪悜浜0)鐨鏋侀檺鐢ㄥ畾涔夋眰lim1/x^2*cosx=0鐨勬瀬闄... 鍒╃敤鏃犵┓灏忕殑绛変环浠ｆ崲娉曟眰limtan3x/sin2x(x瓒嬪悜浜0)鐨勬瀬闄 鐢ㄥ畾涔夋眰lim1/x^2*cosx=0鐨勬瀬闄 灞曞紑 1涓洖绛 #鐑# 涓轰粈涔堢幇鍦ㄦ儏鏅枩鍓ц秺鏉ヨ秺灏戜簡?
