高数8，9，，10题 高数试题，6,8,9,10谁做出来给100
\u9ad8\u6570\uff0c\u5927\u4e00\u30028\u30019\u300110\u7684\u8be6\u7ec6\u89e3\u9898\u6b65\u9aa48. \u4ee4 A=\u222bf(x)dx, \u5f97 f(x)=1/(1+x^2)+Ax^3,
\u4e24\u8fb9\u5728[0,1]\u4e0a\u79ef\u5206\uff0c\u5f97
A = [arctanx]+(A/4)[x^4] = \u03c0/4+A/4,
\u89e3\u5f97 A=\u03c0/3\uff0c\u5373\u222bf(x)dx = \u03c0/3 \u3002
9. \u4e00\u9636\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b\uff0c\u901a\u89e3\u662f
y=e^(-\u222b2xdx)[C+\u222b4xe^(\u222b2xdx)] = e^(-x^2)[C+\u222b4xe^(x^2)dx]
= e^(-x^2)[C+2\u222be^(x^2)dx^2] = e^(-x^2)[C+2e^(x^2)] = 2+Ce^(-x^2).
10. x=0 \u65f6\uff0cy=0. x\uff0cy \u5747\u4e0d\u4e3a\u96f6\u65f6\uff0c
\u7531 xdy=-2ydx, \u5f97 dy/y = -2dx/x, lny = -2lnx+lnC,
\u901a\u89e3\u662f y = C/x^2, \u5373 yx^2=C.
6\u3001x>0\u65f6
\u5229\u7528\u9690\u51fd\u6570\u6c42\u5bfc\uff0c\u5f97\u5230f'(x)
\u6c42\u51fa\u9a7b\u70b9\uff0c\u5f97\u5230f(x)\u7684\u6781\u5c0f\u503c
\u8fc7\u7a0b\uff1a
8\u3001\u6784\u9020\u51fd\u6570\uff0c\u5229\u7528\u5355\u8c03\u6027\u8bc1\u660e
9\u3001\u6784\u9020\u51fd\u6570\uff0c\u5229\u7528f(x)\u5355\u8c03\u9012\u51cf\u8bc1\u660e
10\u3001\u5148\u6c42\u5207\u7ebf\u65b9\u7a0b
\u5229\u7528\u5b9a\u79ef\u5206\u6c42\u9762\u79ef\u548c\u4f53\u79ef
9 10公式
绛旓細8銆侀堿 fx=x^4+1/2x^2+c f(1)=1+1/2+c=-1 鈭碿=-5/2 9銆侀堿锛屾帓闄ゆ硶銆俥=2.718锛宔^0.1<e^1=2.718锛屾帓闄C 1.512>1.5锛岃1.5*1.5*1.5>e锛屽嵆1.512>1.5>e^1/3鎺掗櫎D 10銆侀塀 fx=1/2sin2x-0=1/2sin2x锛宖x'=cos2x锛宖'(PI)=cos2PI=1 ...
绛旓細锛8锛夊埄鐢ㄦ瀬闄愶紳e鐨勯噸瑕佸叕寮忔眰鏋侀檺 寰楀埌f(x)鐨勮〃杈惧紡 鍐嶆眰瀵 锛9锛夊埄鐢ㄧ瓑浠锋棤绌峰皬鏇挎崲 鍙緱f(x)涓巟骞虫柟鏄悓闃舵棤绌峰皬 鍐嶇敱瀵兼暟瀹氫箟鍙緱f'(0)锛0 锛10锛夋眰鍑篺'(x)鐨勫垎娈佃〃杈惧紡 鍐嶅埄鐢ㄥ鍚堝嚱鏁版眰瀵兼硶鍒 姹俤y/dx锛寈锛漞 缁撴灉锛1/e 杩囩▼濡備笅锛...
绛旓細涓嶇煡閬撲綘瑕佺9杩樻槸绗10棰锛屽氨閮藉啓浜嗭細浠ヤ笂锛岃閲囩撼銆
绛旓細8 鐩存帴鐢ㄦ礇蹇呰揪娉曞垯鍗冲彲 鍘熸瀬闄=lim (e^x+1+xe^x-2e^x)/3x^2=lim(xe^x-e^x+1)/3x^2 =lim (e^x+xe^x-e^x)/6x =lim xe^x/6x =lim e^x/6 =1/6 10 涔熸槸鐢ㄦ礇蹇呰揪娉曞垯 鍘熸瀬闄=lim (1-x)/cot(蟺x/2)=lim (-1)/{(蟺/2)[-(csc(蟺x/2))^2]} =lim (2/蟺...
绛旓細9 鍚戦噺AB=(2,-2,-1)鍚戦噺AC=(12,4,7)閭ｄ箞ABxAC=(-10,-26,32)C鍒癆B鐨勮窛绂籨=|ABxAC|/|AB|=30鈭2/3=10鈭2 10 (1)m鈯 閭ｄ箞mn=0 鍗(2a+b)(ka+b)=2k|a|²+(k+2)ab+|b|²=2k+4=0 鎵浠= -2 (2)鐢眒 n鐩搁偦鐨勫洓杈瑰舰闈㈢Н涓 S=|mxn|=|(2a+b)x(ka+...
绛旓細6銆亁>0鏃 鍒╃敤闅愬嚱鏁版眰瀵硷紝寰楀埌f'(x)姹傚嚭椹荤偣锛屽緱鍒癴(x)鐨勬瀬灏忓 杩囩▼锛8銆佹瀯閫犲嚱鏁帮紝鍒╃敤鍗曡皟鎬ц瘉鏄 9銆佹瀯閫犲嚱鏁帮紝鍒╃敤f(x)鍗曡皟閫掑噺璇佹槑 10銆佸厛姹傚垏绾挎柟绋 鍒╃敤瀹氱Н鍒嗘眰闈㈢Н鍜屼綋绉
绛旓細9 10鍏紡
绛旓細2sina<=p<=4sina aE[0,pai]鍘熷紡=鈭(0,pai)da鈭(2sina,4sina)p*pdp =鈭(0,pai) [1/3*(64sin^3a-8sin^3a)]da =-56/3*鈭(0,pai) (1-cos^2a)dcosa =-56/3*[cosa-1/3cos^3a] (0,pai)=-56/3*[-1+1/3-(1-1/3)]=-56/3*(-4/3)=224/9 8;y=(1-x^2...
绛旓細8. 鍘熷紡=2lim锛坸鈫0锛塠f锛坸锛-f锛-x锛塢/2x =2lim锛坸鈫0锛塠f锛坸锛-f锛-x锛塢/锛坸-[-x]锛=2f鈥橈紙0锛=2脳1 =2 9 鍘熷紡=鈭紙-1,1锛墄³/锛1锛媥²锛塪x 鍥犱负琚Н鍑芥暟鏄鍑芥暟锛屽埄鐢ㄥ伓鍊嶅闆 锛嬧埆锛-1,1锛1/锛1锛媥²锛塪x 杩欏効鏄伓鍑芥暟 =2鈭紙0...
绛旓細y=锛坸-1锛夛紙x+1锛/锛坸-1锛夛紙x-2锛夛紝x=1锛寈=2鏄棿鏂偣锛屼絾鏄紝濡傛灉x鈮1锛寈-1鍙互绾﹀幓锛寉=锛坸+1锛/锛坸-2锛夛紝鍙琛ュ厖瀹氫箟锛寈=1鏃讹紝y=锛坸+1锛/锛坸-2锛,鍑芥暟鍦▁=1灏辨槸杩炵画鐨勶紝x=2涓嶅彲鍘汇傦紙2锛墄=k蟺鏃讹紝tanx=0锛屽垎姣嶄负0锛屾槸闂存柇鐐癸紝鍦ㄨ鐐逛袱渚э紝tanx鐨勫煎紓鍙凤紝鎺ヨ繎浜...
