lim(tanx-sinx)/x(1-cosx) lim((x→0) (sinx/x)^1/(1-cosx)
lim\uff08tanx-sinx\uff09/x
\u5982\u56fe\u6240\u793a
\u7b80\u5355\u8ba1\u7b97\u4e00\u4e0b\u5373\u53ef\uff0c\u7b54\u6848\u5982\u56fe\u6240\u793a
lim (tanx-sinx)/x (x→0)
=lim sec^2x-cosx)(x→0)
=1-1=0
lim (1-cos4x)/xsinx (x→0)
=lim (1/2)*16x^2/x^2 (x→0)
=8
绛旓細棣栧厛锛tanx-sinx鍦0澶勭殑鏋侀檺涓0锛屼絾鍋氭硶涓嶆槸tanx~x锛宻inx~x锛寈-x=0銆傛纭В娉 涔橀櫎绛変环鏃犵┓灏忔槸鍙互杩涜鏇挎崲鐨勶紝鍔犲噺鍦ㄦ弧瓒充竴瀹氱殑鏉′欢鐨勬儏鍐典笅鏄彲浠ヨ繘琛屾浛鎹㈢殑銆傛潯浠跺涓嬶細鍔犳硶閫傜敤鏉′欢 鍑忔硶閫傜敤鏉′欢 鑻ュ府鍒版偍璇烽噰绾虫垜鐨勭瓟妗堬紝璋㈣阿锛
绛旓細tanx-sinx=2tan(x/2)/(1+tan^2(x/2))-2tan(x/2)/(1+tan^2(x/2)),閫氬垎鍚庯紝寰楀嚭tanx-sinx=4tan^3(x/2)/(1-tan^4(x/2))褰搙瓒嬭繎浜0鏃讹紝tanx瓒嬭繎浜0銆傛晠褰搙瓒嬭繎浜0鏃讹紝lim(tanx-sinx)=0
绛旓細lim (tanx-sinx)/(x^2*sinx) = limtanx (1-cosx)/(x^2*sinx) (绛変环鏃犵┓灏忎唬鎹) = limx (x^2/2)/(x^2*x) = 1/2
绛旓細lim(x->0) [tan(tanx) -sin(sinx)]/(tanx-sinx)甯﹀叆浠ヤ笂绛変环 =lim(x->0) x^3/[ (1/2)x^3]=2
绛旓細tanx-sinx=tanx(1-cosx)lim (tanx-sinx)/sinx =lim tanx(1-cosx)/x =lim x(x鏂/2)/x =0 鎵浠 tanx-sinx鏄痵inx鐨勯珮闃舵棤绌峰皬.
绛旓細鏂规硶濡備笅锛岃浣滃弬鑰冿細
绛旓細=lim (1+cosx+cos²x)/cos²x x鈫0 =(1+1+1²)/1²=3 瑙ｆ硶浜岋細绛変环鏃犵┓灏 lim (tanx-sinx)/(x-sinx)x鈫0 =lim [(x+⅓x³)-(x- x³/6)]/[x-(x- x³/6)]x鈫0 = lim ½x³/(x³/6)x鈫0 =3 涓ょ鏂规硶...
绛旓細x鈫0鏃讹紝lim(tanx-sinx)/x³锝烇綖锝//娲涘繀杈炬硶鍒欐渶鐩存帴// //涓鐩存礇涓嬪幓锛岀洿鍒颁笉鑳芥礇涓烘// x鈫0鏃讹紝lim(tanx-sinx)/x³=lim(sec²x-cosx)/3x²=lim(2secxtanxsecx+sinx)/6x =lim(2sec²xtanx+sinx)/6x =lim[(2sec³x+1)/6]鈼廩sinx/x]=[(2...
绛旓細tanx-sinx=tanx(1-cosx)~x路1/2路x^2=1/2路x^3 arctan(a^3)~x^3 lim(tanx-sinx)/arctanx^3 =lim(1/2路x^3/x^3)=1/2
绛旓細lim(tanx-sinx)/sinx^3 绛変环鏃犵┓灏忎唬鎹細sinx~x lim(tanx-sinx)/x^3 tanx-sinx=sinx/cosx-sinx=sinx(1-cosx)/cosx=sinx(2sin(x/2锛²/cosx=x*(x/2锛²/1=x³/2 鎵浠ュ師寮 =1/2x³/x³=1/2
