2017年春國家開放大學(xué)《經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)》任務(wù)1參考答案
2017年春國家開放大學(xué)“經(jīng)濟(jì)數(shù)學(xué)基礎(chǔ)”任務(wù) 1參考答案填空題必須手寫答案后拍照上傳!若直接將提供的電子文檔答案截圖上傳,則成績按0分計算! !切記,切記! !、填空題x sin x.答案:2 .設(shè) f(x)xx2 1, x 0,在x 0處連續(xù),則k, x 0.答案:13.曲線y Q +1在(1,2)的切線方程是-1.答案:y 1x 24.設(shè)函數(shù) f(x 1) x2 2x 5,則 f (x).答案:2x.答案:-,冗5.設(shè) f (x) xsin x ,則 f (-) 2二、單項選擇題1.當(dāng)x時,下列變量為無窮小量的是(A. ln(1 x)2xB.x 1C.1e x2sin xD.xA. lim 一x 0 x3.設(shè) y lg2 x ,則 dy).A. -dx B. -1 2xx ln10dxC.4.若函數(shù)f (x)在點xo處可導(dǎo),則ln10 , dxx)是錯誤的.D.-dx xA .函數(shù)f (x)在點xo處有定義B. lim f (x)X x0A,但Af (xo)C.函數(shù)f (x)在點xo處連續(xù)D.函數(shù)f (x)在點xo處可微2.下列極限計算正確的是(B. lim 一x 0 xsin xD. hm. 1,C.lim xsin - 15.當(dāng) f A 1C 11A 2B 2C .一XXX X,則f (x)( B ).D.X解答題必須手寫解題步驟后拍照上傳!若直接將提供的word文檔答案截圖上傳,則成績按0分計算! !切記,切記! !三、解答題i .計算極限(1)limX 1X2 3x 2x2 1limX 1(x 2)(x 1)(x 1)(x 1)一 x 2=lim X 1 (x 1)(2)limX 2x2 5xx2 6x一 =lim8 x 2(X 2)(x 3)(x 2)(x 4)x 3 limX 2 (x 4)(3)limX 01 = limX 0(1 X 1)( ,1 XX( . 1 X 1)1)(4)limX(5)limX 0(6)limX 2= limX 0X( .1X2 3x 53x2 2x 4sin3xsin 5xX 1)= lim1 X 0 (,1 x 1)1 3 lim x x 3 2X5-2 X4-2 X5xsin3x3 3 lim=X 03xsin5x5 5X24sin(x 2)lim (X 2)(X 2) 4X 2 sin(x 2)2.設(shè)函數(shù)f (x)00,0xsin b, xXa, x sin x XX問:(1)當(dāng)a,b為何值時,f (x)在x 0處有極限存在?(2)當(dāng)a,b為何值時,f(x)在X 0處連續(xù).解:(1)要使 “乂)在乂 0處極限存在,則必有州f(x)lim f (x)x 0又呵f (x)limx 0sin x 1xlim f (x)x 0limx 0xsin1 b bx即b=1所以當(dāng)a為實數(shù),b=1時,f(x)在x=0處極限存在(2)要使 “乂)在乂 0處連續(xù),則必有l(wèi)im f (x) f (0)= a x 0當(dāng)a b 1時,f (x)在x0處連續(xù)。3.計算下列函數(shù)的導(dǎo)數(shù)或微分:(1)x2 2x log 2 x 22,解:(2)解:y = a(cx d) c(ax b)(cx d)2ad cb(cx d)2x12x 2xln 2 -xln 2ax b /,求ycx d(3)解:1=(3x3x 55)2(3x 5)3(4)解:1 (x 1)e2 : x(5)eax sin bx ,求 dy解:(eax) sin bx eax(sin bx)_ _ axaxae sin bx e cosbx bdyax 一 一e (asin bx bcosbx)ax 一 一 一 一一一e (a sinbx bcosbx)dx(6)1exx>/x,求 dy解:dy(卡1 1-ex)dx xcos xx2,e ,求 dy解:dy2(2xe xsin 一 x.)dx2 x(8) n vsin xsin nx,求 y解:n 1y - nsinxcosx+cosnxn=n(sin n 1 xcosx cosnx)(9)ln(x 71 x2),求 y解:(10)解:y1 cot 一2 xx2(x.1 x2)x2(11x2) 2 2x)xTx2 (11 3 x2 2x、又1cot-2 x ln 22.1x sin 一x一x) .1 x2)51 g-x 664.下列各方程中y是x的隱函數(shù),試求y或dy(1) x2y2 xy 3x 1 ,求 dy解:方程兩邊關(guān)于 x求導(dǎo):2x 2yy y(2yx)y y 2x 3 ,dy3dx2y x(2) sin(xy) exy 4x ,求 yxy解:解:方程兩邊關(guān)于 x求導(dǎo)cos(x y)(1 y ) exy(y xy ) 4(cos(x y) exyx)y 4 yexycos(x y)4 yexy cos(x y) 丫 xexy cos(x y)5.求下列函數(shù)的二階導(dǎo)數(shù):2、(1) y ln(1 x ),求 yI + .V1.2,2。-2Mo + 2外 2-2jj,二E 二(TT77二 E所以y (1) 1?x 0 x1 卡*,求 y3x 5