f(x)=lnx+x²的函数图像怎么画 函数图像y=x+lnx怎么画？必采。
\u51fd\u6570f(x)=lnx-x\u7684\u56fe\u50cf\u7531f'(x)=1/x-1=0\u5f97x=1\uff0c\u4e14x>1\u65f6f'(x)0\uff0c\u6545f(x)=lnx-x\u5728(0,1)\u4e0a\u662f\u589e\u51fd\u6570\uff0cf(x)=lnx-x\u5728(1\uff0c+\u221e)\u4e0a\u662f\u51cf\u51fd\u6570\uff0c\u7ed3\u5408\u5b9a\u4e49\u57df\uff0c\u53ef\u4ee5\u753b\u51faf(x)=lnx-x\u7684\u8349\u56fe\u5982\u56fe\u6240\u793a
\u51fd\u6570 y = x+lnx \u7684\u5b9a\u4e49\u57df\u4e3a x > 0\u3002
\u56fe\u50cf\u5982\u4e0b\uff1a
绛旓細姹傚鍑芥暟 f鈥(x)= 1-lnx x 2 鐢眆鈥诧紙x锛=0鍙緱1-lnx=0鈭磝=e鈭祒鈭堬紙0锛宔锛夛紝f鈥诧紙x锛夛紴0锛寈鈭堬紙e锛+鈭烇級锛宖鈥诧紙x锛夛紲0锛屸埓x=e鏃讹紝鍑芥暟f锛坸锛= lnx x 鍙栧緱鏈澶у间负 1 e 鏁呯瓟妗堜负锛 1 e ...
绛旓細鍦▁=2澶勶紝f(x)=lnx鐨勫洓闃舵嘲鍕掑叕寮忎负锛歭nx=ln2+(x-2)/2-(x-2)^2/8+(x-2)^3/24-(x-2)^4/64+(x-2)^5/160[1+a(x-2)/2]^5 (0<a<1)杩欐槸鍥犱负鎴戜滑鐭ラ亾锛屽湪x=0澶勶紝ln(1+x)鐨勫睍寮鍏紡涓猴紙鍥涢樁涓轰緥锛塴n(1+x)=x-x^2/2+x^3/3-x^4/4-x^5/5(1+ax)^5 (...
绛旓細x鈫0+锛f(x)=lnx鈫-鈭烇紝杩欐椂f(x)鏄礋鏃犵┓澶с倄鈫+鈭烇紝f(x)=lnx鈫+鈭烇紝杩欐椂f(x)鏄鏃犵┓澶с備互涓嬫槸鏃犵┓澶х殑鐩稿叧浠嬬粛锛氬湪闆嗗悎璁轰腑瀵规棤绌锋湁涓嶅悓鐨勫畾涔夈傚痉鍥芥暟瀛﹀搴锋墭灏旀彁鍑猴紝瀵瑰簲浜庝笉鍚屾棤绌烽泦鍚堢殑鍏冪礌鐨勪釜鏁帮紙鍩烘暟锛夛紝鏈変笉鍚岀殑鈥滄棤绌封濄備袱涓棤绌峰ぇ閲忎箣鍜屼笉涓瀹氭槸鏃犵┓澶э紝鏈夌晫閲忎笌鏃犵┓...
绛旓細f(x)=lnx 灞曟垚 x0 = 2 澶勭殑Taylor鍏紡锛圥eano浣欓」锛夈傚埄鐢 ln(1+x) = x - x²/2 + x³/3 + ... + (-1)^(n-1) x^n /n + o(x^n)f(x) = lnx = ln [ 2 + (x-2) ] = ln2 + ln [ 1 + (x-2)/2 ]= ln2 + (x-2)/2 - (x-2)²...
绛旓細f(x)=lnx鐨勫嚱鏁板浘鍍忔槸涓鏉¤繃I锛孖V璞￠檺鐨勫鏁板嚱鏁版洸绾匡紝鏄竴鏉″畾涔夊煙鍦(0,+鈭)锛屽煎煙鍦≧涓婏紝鍗曡皟閫掑鐨勬洸绾裤傛洸绾跨粡杩(1,0)锛屼笖鍚戜笂鍑歌捣銆俵nx鐨勬ц川锛1銆佸畾涔夊煙涓簒鈭(0,+鈭)锛屽煎煙涓(-鈭,+鈭)锛屽浘褰㈠垎甯冨湪涓鍥涜薄闄愶紱涓哄崟璋冮掑锛岄潪濂囬潪鍋躲2銆佷粠瀵兼暟鏉ョ湅鍗曡皟鎬х湅璧锋潵鏇村揩y'=lnx-1锛/...
绛旓細f(x)=lnx鐨勫師鍑芥暟鏄疐(x)=xlnx-x+C銆傞鍏堬紝鎴戜滑闇瑕佹壘鍒癴(x)=lnx鐨勫師鍑芥暟锛屼篃灏辨槸姹傚叾涓嶅畾绉垎銆備娇鐢ㄥ垎閮ㄧН鍒嗘硶锛屾垜浠护u=lnx锛宒v=dx锛屽垯du=dx/x锛寁=x銆傚洜姝わ紝鍘熷嚱鏁癋(x)鍙互琛ㄧず涓猴細F(x) = xlnx - ∫xd(lnx)= xlnx - ∫x*(1/x)dx = xlnx - ∫dx = xlnx...
绛旓細u(x)=f(x)-t u'(x)=f'(x)=(1-lnx)/x^2>0 lnx<1 0<x<e,澧炵殑. x>e鍑忕殑. 鏈澶у紆(e)=lne/e-t=1/e-t 鐢变簬u(x)寮鍙ｅ悜涓,fx)-t=0鍦╗1/e锛宔^2]涓婃湁涓や釜涓嶅悓鐨勮В,鍒:u(1/e)<=0 u(e^2)<=0 涓攗(x)max>0 鍗:u(1/e)=ln(1/e)/(1/e)...
绛旓細杩欐槸姹傚鍚堝嚱鏁扮殑瀵兼暟,f(f(x))=lnx 涓よ竟姹傚 寰楋細f(f(x))f`(x)=1/x 鎶奻(f(x))=lnx浠ｅ叆涓婂紡 寰楋細f`(x)=1/xlnx
绛旓細鍏堢湅x瀹氫箟鍩燂紝鐢眑nx鍙煡x锛0,寰梕x+x锛瀍,涓斾负澧炲嚱鏁 鍒f(x)=x*lnx=ln(ex+x)锛1,鎵浠ュ嚱鏁癴(x)鍥惧儚搴斾负杩囷紙0,1锛夌偣浣嗕笉鍚紙0,1锛夌偣鐨勫鍑芥暟
绛旓細鎸夌収杩炵画鐨勫畾涔夛紝鍙璇佹槑瀵逛竴鍒噚>0锛屻怢im锛堚棁x鈫0锛塮锛坸+鈼噚锛夈=f锛坸锛夋垚绔嬨傛敞鎰忓埌瀵规暟鍑芥暟婊¤冻f锛坸+鈼x锛=f锛坸锛*f锛堚棁x锛夋晠鑰屼笂闈㈢殑銆愨︺=Lim锛堚棁x鈫0锛塮[x锛1+鈼噚/x锛塢=Lim[f锛坸锛*f锛1+鈼噚/x锛塢=f锛坸锛夌洊鍥燣im锛坔鈫0锛塮锛1+h锛=f锛1锛=0(杩欐槸鐢ㄧ殑f鍦▁=...
