函数f(x)=lnx在(1,0)的切线方程 函数f（x）=lnx的图象在点x=1处的切线方程是_____...
\u51fd\u6570f\uff08x\uff09=lnx\u7684\u56fe\u8c61\u5728\u70b9x=1\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u662f______\u628ax=1\u4ee3\u5165f\uff08x\uff09=lnx\u5f97\uff0cf\uff081\uff09=ln1=0\uff0c
\u2234\u5207\u70b9\u7684\u5750\u6807\u4e3a\uff1a\uff081\uff0c0\uff09\uff0c
\u7531f\u2032\uff08x\uff09=\uff08lnx\uff09\u2032=1x\uff0c\u5f97\u5728\u70b9x=1\u5904\u7684\u5207\u7ebf\u659c\u7387k=f\u2032\uff081\uff09=1\uff0c
\u2234\u5728\u70b9x=1\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a\uff1ay=x-1\uff0c
\u6545\u7b54\u6848\u4e3a\uff1ay=x-1\uff0e
\u628ax=1\u4ee3\u5165f\uff08x\uff09=lnx\u5f97\uff0cf\uff081\uff09=ln1=0\uff0c\u2234\u5207\u70b9\u7684\u5750\u6807\u4e3a\uff1a\uff081\uff0c0\uff09\uff0c\u7531f\u2032\uff08x\uff09=\uff08lnx\uff09\u2032=1x\uff0c\u5f97\u5728\u70b9x=1\u5904\u7684\u5207\u7ebf\u659c\u7387k=f\u2032\uff081\uff09=1\uff0c\u2234\u5728\u70b9x=1\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3a\uff1ay=x-1\uff0c\u6545\u7b54\u6848\u4e3a\uff1ay=x-1\uff0e
y＝x-1
Y =x _1
先将函数求导
绛旓細B y`=lnx+x/x=1+lnx=0 x=1/e 1>x>1/e y`>0 y鏄鍑芥暟 0<x<1/e y`<0 y鏄噺鍑芥暟
绛旓細瑙ｇ瓟锛歠(x)=xlnx 鈭 f'(x)=lnx+x*(1/x)=1+lnx 鈭 f(x)鍥惧儚 x=1澶勫垏绾挎枩鐜噆=f'(1)=1 鍒囩偣(1,0)鈭 鍒囩嚎 绋 y=x-1 鍗 x-y+1=0 鍦唜^2+y^2=1/2 鍦 O(0,0)鍗婂緞R 鈭2/2 鍦 鐩寸嚎x-y+1=0 璺濈d=|0-0+1|/鈭2=鈭2/2=R 鈭 鍑芥暟f(x)=xlnx 鍥惧儚 x=1澶...
绛旓細鍦 x=1 澶勶紝宸﹀彸鏋侀檺閮=0=f(1)锛屽洜姝よ繛缁紱宸﹀鏁= - 1锛屽彸瀵兼暟=1锛鍥犳涓嶅彲瀵笺
绛旓細瑙ｇ瓟:瑙:(1)f鈥(x)=(lnx)鈥= 1 x 锛屸埓鍒囩嚎鐨勬枩鐜囦负k=f'(1)=1锛屸埓鍒囩嚎鏂圭▼涓簓-0=x-1 鍗硑=x-1 .(2)g(x)=(1-x)f(x)=lnx-xlnx锛屸埓g鈥(x)= 1 x -lnx-1锛屸埓h鈥(x)=- x+1 x2 锛0鍦(1锛+鈭)涓婃亽鎴愮珛锛屸埓h(x)鍦(1锛+鈭)涓婂崟璋冮掑噺锛屸埓g'(x)锛瀏'(1)=0...
绛旓細鍦 x>a 锛坅>0,a涓轰竴鍥哄畾鐨勬暟锛夌殑瀹氫箟鍩熶笂,ln(x) 涓鑷存敹鏁涳紱褰 x>a 鏃,鍥犱负ln(x)鏄繛缁鍑芥暟,褰搙瓒嬩簬1鏃,ln(x)瓒嬩簬0,鍗 浠诲彇e>0,瀛樺湪d>0,浣垮緱褰搢x-1|a,褰搢x2-x1|a鐨勬儏鍐典笅,ln(x) 涓鑷存敹鏁.鑷劧鏈f(x)=lnx鍦[1,+鈭)涓婁竴鑷磋繛缁.
绛旓細鈭礷锛坸锛=xlnx锛屸埓f鈥锛坸锛=lnx+1锛鍒檉鈥锛1锛=1锛庡張褰搙=1鏃秄锛1锛=0锛屸埓鍑芥暟f锛坸锛=xlnx鍦▁=1澶勭殑鍒囩嚎涓簓-0=1脳锛坸-1锛夛紟鍗硑=x-1锛庢晠閫夛細B锛
绛旓細鎵浠ョ洿绾縧鐨勬柟绋嬩负x-y-1=0锛庯紙6鍒嗭級锛堚叀锛塯锛坸锛=xlnx-a锛坸-1锛锛屽垯g鈥锛坸锛=lnx+1-a锛岋紙7鍒嗭級瑙鈥诧紙x锛=0锛屽緱x=ea-1锛鎵浠ュ湪鍖洪棿锛0锛宔a-1锛変笂锛実锛坸锛変负閫掑噺鍑芥暟锛屽湪鍖洪棿锛坋a-1锛+鈭烇級涓婏紝g锛坸锛変负閫掑鍑芥暟锛庯紙8鍒嗭級褰揺a-1鈮1锛屽嵆a鈮1鏃讹紝鍦ㄥ尯闂碵1锛宔]涓婏紝...
绛旓細鍑芥暟f(x)鍦鍖洪棿D涓婇掑噺锛屽垯搴旇鏄細f'(x)鈮0鍦ㄥ尯闂碊涓婃亽鎴愮珛銆傛湰棰樹腑锛宖'(x)=(1/x)锛(k/x²)鈮0锛屽叾涓0<x<1 鍒欙細k鈮 鍒欙細k鈮鍦ㄥ尯闂(0锛1)涓婄殑鏈澶у0锛屽垯锛歬鈮1 鍥犱负鏈涓槸锛氬嚱鏁癴(x)鐨勯掑噺鍖洪棿鏄(0锛1)锛鏄剧劧搴旇鏄細f'(1)=0锛屽緱锛歬=1 ...
绛旓細缁撴灉涓猴細-1 瑙ｉ杩囩▼濡備笅锛氬師寮=x*lnx-鈭锛1/x)*xdx =xlnx-x+lnx dx =鈭 [0,1] lnx dx =xlnx [0,1]-鈭 [0,1] x*(1/x) dx =0-鈭 [0,1] 1 dx =-1
绛旓細閴翠簬浣犳病瀛﹀鏁,鍦ㄦ鎴戝氨鐢ㄥ垵绛夋暟瀛︽潵鍋氫簡,涓嶈繃涓嶇鐢ㄤ粈涔堟柟娉,涓瀹氫細娑夊強鍒拌嚜鐒跺簳鏁癳,鍦ㄦ瑕佸厛寮曞叆e鐨勫畾涔夊紡,e=lim[x->鈭瀅(1+1/x)^x,姝ゅ[]琛ㄧず涓嬫爣,lim琛ㄧず鏋侀檺.y=x^x=e^(xlnx)浣滀唬鎹=1/x y=e^(ln(1/t)/t)=e^(-lnt/t)鑰冨療鍑芥暟f(x)=lnx/x 杩欎釜鍑芥暟鐨勫嚑浣曟剰涔夋槸y=lnx...
