极限题limx立方加x除x四次幂减3x方加一limx 0tanx-sinx/x3
\u901f\u6c42\u6781\u9650\u95ee\u9898 limx\u21920 \uff08sinx-xcosx\uff09/sin^3x\u7684\u6781\u9650 \u8bf7\u5199\u8fc7\u7a0blimx\u21920
\uff08sinx-xcosx\uff09/sin^3x
=(1-xcotx)/sin²x
=\uff08tanx-x\uff09/x³ \u5229\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\uff1asinx\u223dx\u223dtanx
=\uff08sec²x-1\uff09/3x² \u6d1b\u5fc5\u8fbe\u6cd5\u5219\uff0c\u4e0a\u4e0b\u6c42\u5bfc
=tan²x/3x²
=1/3 \u5229\u7528\u7b49\u4ef7\u65e0\u7a77\u5c0f\uff1ax\u223dtanx
1)sinx\uff5ex\uff08x\u21920\uff09
2)e^x-1\uff5ex\uff08x\u21920\uff09
3)(1+x)^a-1\uff5eax\uff08x\u21920\uff09
4)1-coxx\uff5e1/2x^2\uff08x\u21920\uff09
5)e^x-1\uff5ex\uff08x\u21920\uff09
6)lnx\uff5ex-1\uff08x\u21920\uff09
\u5728\u6c42\u6781\u9650\u65f6\u5982\u679c\uff08x\u21920\uff09\u53ef\u4ee5\u628a\u524d\u9762\u7684\u7b49\u4ef7\u4e8e\u540e\u9762\u7684\u5e26\u5165
\u4f8b\uff1alim[(sinx)/(x+x^2+3x^3)] =lim[x/(x+x^2+3x^3)]
绛旓細绠鍗曡绠椾竴涓嬪嵆鍙紝绛旀濡傚浘鎵绀
绛旓細(x²+x)^x=x^x*[(1+x)^x]鍏朵腑x^x=x^0=1锛(1+x)^x=1 寰楀嚭鏋侀檺涓1
绛旓細鍙鎷嗗紑鐨2閮ㄥ垎锛屼粬浠殑鏋侀檺閮藉瓨鍦紝灏卞彲浠ユ媶寮
绛旓細lim(x->鏃犵┓) (x^3-x^2+1)/(x^3-x+1)=lim(x->鏃犵┓) (1-1/x+1/x^3)/(1- 1/x^2+1/x^3)=1
绛旓細娲涙瘮杈炬硶鍒
绛旓細1棰.鍘熷紡=lim(x->+鈭){[1-2/(3x)]^(4x+1)} =lim(x->+鈭){[1+(-2)/(3x)]^[(3x)/(-2)]}^[(-2)(4x+1)/(3x)]} =e^{lim(x->+鈭){[(-2)(4x+1)/(3x)]} (鍒╃敤鐗规畩鏋侀檺)=e^锛-8/3锛2棰.鍘熷紡=lim(x->+鈭){[1+(-1)/(1+x)]^(-2x+1)} =lim(...
绛旓細鍏蜂綋鍥炵瓟濡備笅锛lim(x鈫0+)(x^x)=lim(x鈫0+) e^ln(x^x)=lim(x鈫0+) e^(xlnx)=e^lim(x鈫0+) (xlnx)=e^0 =1 鏋侀檺鐨勬剰涔夛細涓鑸潵璇达紝N闅徫电殑鍙樺皬鑰屽彉澶э紝鍥犳甯告妸N鍐欎綔N(蔚)锛屼互寮鸿皟N瀵刮电殑鍙樺寲鑰屽彉鍖栫殑渚濊禆鎬с備絾杩欏苟涓嶆剰鍛崇潃N鏄敱蔚鍞竴纭畾鐨勶細锛堟瘮濡傝嫢n>N浣縷xn-a...
绛旓細鍏跺疄姹傛瀬闄愰棶棰橀潪甯哥畝鍗曪紒棣栧厛浣犺璁颁綇甯歌鐨勭瓑浠锋浛鎹㈠舰寮忥紝姣斿锛歺鈫0锛歺~sinx~tanx;n娆℃牴鍙蜂笅锛1+x锛墌1+x/n 姝ゅ灏辨槸涓や釜鏈閲嶈鐨勶細lim x鈫0(1+x)鐨1/x娆=e lim x鈫掓棤绌峰ぇ[1+(1/x)]鐨剎娆=e 鎴戝凡缁忓緢闀挎椂闂存病鐪嬭繖鏂归潰鐨勪笢瑗夸簡锛岃繕鏈夊叾瀹冧竴浜涚瓑浠锋浛鎹備笂闈㈢殑鍚庨潰涓や釜瀹炶川涓婃槸涓...
绛旓細鏈鍚庝竴棰樻棤娉曡绠
绛旓細鍒嗘瘝瓒嬩簬0鑰屾瀬闄愬瓨鍦 鎵浠ュ垎瀛愯秼浜0 鎵浠x=-1 x³-ax²-x+4=-1-a+1+4=0 a=4 x³-4x²-x+4=(x-4)(x+1)(x-1)鍒欏嵆lim(x-4)(x-1)=b (-1-4)(-1-1)=b 鎵浠 a=4锛宐=10
