sinx∧2在X趋近于0如何求导
\u5fae\u79ef\u5206\uff0cx-sinx/x^2 x\u8d8b\u4e8e0\uff0c\u600e\u4e48\u7b97\u7684\uff1flim(x->0)(x-sinx/x^2)=lim(x->0)(x)-lim(x->0)(sinx/x^2)=0-lim(x->0)(cosx/2x),
x\u8d8b\u4e8e0+\uff0c\u503c\u4e3a-\u221e
x\u8d8b\u4e8e0-\uff0c\u503c\u4e3a\u221e
y=(1+x)^(2/sinx)lny=2/sinx*ln(1+x)=2ln(1+x)/sinx0/0\u578b\u7528\u6d1b\u6bd4\u8fbe\u6cd5\u5219\u5206\u5b50\u6c42\u5bfc=2/(1+x)\u5206\u6bcd\u6c42\u5bfc=cosx\u6240\u4ee5\u662f2/(1+x)cosx\u6240\u4ee5lny\u6781\u9650\u662f2\u6240\u4ee5\u539f\u5f0f=e²
函数及其导数均有定义，直接将自变量值代入导函数求就行；sin(x²) → [sin(x²)]'=cos(x²)*(x²)'=cos(x²)*2x；当 x→0，[sin(x²)]'→2*0*cos(0²)=0；
如为 sin²x → (sin²x)'=2sinx*(sinx)'=2sinx*cosx；当 x→0，[sin²x]'→2sin0cos0=0；
绛旓細鍑芥暟鍙婂叾瀵兼暟鍧囨湁瀹氫箟锛岀洿鎺ュ皢鑷彉閲忓间唬鍏ュ鍑芥暟姹傚氨琛岋紱sin(x²) 鈫 [sin(x²)]'=cos(x²)*(x²)'=cos(x²)*2x锛涘綋 x鈫0锛孾sin(x²)]'鈫2*0*cos(0²)=0锛涘涓 sin²x 鈫 (sin²x)'=2sinx*(sinx)'=2sinx*cosx锛涘綋 x鈫...
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绛旓細x瓒嬩簬0鏃讹紝x^2涔熻秼浜0锛屽洜姝sinx^2绛変环浜巟^2锛屽洜姝ゅ師寮=1/x锛岃秼浜庢棤绌凤紝锛堟垨鑰呮瀬闄愪笉瀛樺湪锛岀湅浣犱滑鐨勬暀鏉愭庝箞璇存槑浜嗭級
绛旓細lim(x鈫0) sinx² / x = lim(x鈫0) sinx² / x² * x = lim(x鈫0) sinx² /x² * lim(x鈫0) x = 1 脳 0 銆愰噸瑕佹瀬闄 lim(x鈫0) sinx /x = 1銆= 0
绛旓細lim(x鈫0) sinx² / x = lim(x鈫0) sinx² / x² * x = lim(x鈫0) sinx² /x² * lim(x鈫0) x = 1 脳 0 銆愰噸瑕佹瀬闄 lim(x鈫0) sinx /x = 1銆= 0
绛旓細涓闃跺鏁=2sinx*cosx=sin2x 浜岄樁瀵兼暟=2cos2x 涓夐樁瀵兼暟=-4sin2x 鍥涢樁瀵兼暟=-8cos2x 浜旈樁瀵兼暟=16sin2x 鍏樁瀵兼暟=32cos2x 鎵浠ワ細f(0)鍏樁瀵=32
绛旓細杩囩▼濡備笅锛氬仛鎭掔瓑寮忓彉鎹(sinx)^x=e^(xlnsinx) a^b=blna 绛変笅鏃犵┓灏 =e^(xlnx) sinx~x x-->0鏃 娲涘繀杈炬硶鍒 =e^0 =1
绛旓細缁撴灉鏄1銆傛瀬闄恖im锛x瓒嬭繎浜0+锛夋椂x鐨剆inx娆℃柟鐨勬瀬闄愭眰娉曞涓嬶細璁緔=x^sinx lny=sinx*lnx =lnx/(1/sinx)鍒╃敤娲涘繀杈炬硶鍒 =(1/x)/(-cosx/sin^x)=-sin^x/xcosx =2sinxcosx/(cosx-xsinx)鎶妜=0浠ｅ叆 =0 鎵浠ny鐨勬瀬闄愭槸0 鍥犳y瓒嬩簬1 鎵浠鐨SINX娆℃柟鐨勬瀬闄愭槸1 ...
绛旓細鍏堝埄鐢ㄧ瓑浠锋棤绌峰皬鏇挎崲鍒嗗瓙涓殑sinx鎹㈡垚x锛屽緱锛氬師寮=lim(x鈫0)锛坸锛夊钩鏂 / (2sin0.5*sin0.5x+xsinx)鍐嶅垎瀛愬垎姣嶅悓鏃堕櫎浠ワ紙x锛夊钩鏂癸紝寰楋細=lim(x鈫0) 1/ (2sin0.5*sin0.5x/xx+sinx/x)浠ヤ笅鍒╃敤閲嶈鏋侀檺lim(x鈫0)(sinx/x) =1锛屽緱缁撴灉涓2/3銆傛棰樹篃鍙互鐢ㄦ礇蹇呰揪娉曞垯姹傚嚭銆
绛旓細褰X瓒嬭繎浜0鏃sinx/x瓒嬭繎浜1
