中財金融學考研微積分課程考研試題

1、中財金融學考研微積分課程考研試題一、單選題1. 已知函數(shù)f(x)=(x-1)(x-2)(x-3)(x-4)，則方程f' (x)=0有A.三個根，分別位于區(qū) 間(1,2)、(2,3)、(3,4)內 B.四個根，分別為 x_仁 1,x_2=2,x_3=3,x_4=4C.四個根，分 別位于區(qū)間內(1,2)、(2,3)、(3,4)D.三個根，分別位于區(qū)間(1,2)、(1,3)、(1,4)內2. 過曲線 y=(x+4)/(4-x)上一點(2,3)的切線斜率為 A.-2B.2C.-1D.13. 若 f' (1)=3，則 lim_(h->0)(f(1)-f(1-2h)/h=A.3B.-

2、3C.6D.-64. 下列廣義積分中，發(fā)散的是()A.i nt_M(+oo)xeA(-x)dxB.i nt_eA(+oo)(dx)/(xl nx)C.i nt_M(+oo)xA (2) eA(-x)dxD.i nt_eA(+oo)(dx)/(xl nA(2)x)5. 設 f(x+1)=xA2-3x+2，貝U f(x)=A.xA2-6x+5B.xA2-5x+6C.xA2-5x+2D.xA2-x二、填空題1.lim_(n->oo)sqrt(n)(sqrt(n+1)-sqrt(n)=2. f(x)=(ax+b,x<=1),(xA2,x>1):在 x=1 處可導，則 a=,b=3.

3、f(x)=(x-1,x<0),(xA2,x>0):, J則 lim_(x->0A(-)f(x)=_4. z=xAy，則(delz)/(delx)=,(delz)/(dely)=5. 設 D=(x,y)|x|v=pi,0<=y<=1，則 intint_D(2+xy)dxdy=6. 設有方程 zA2-3xyz-aA3=0則 z' _x=7若 R(x)=10x-0.02xA2，貝U MR=_8. sum_(n=1)A(oo)(2/3)A(n)=9. 已知 lim_(x->oo)(x+a)/(x-a)Ax=eA4，貝U a=10. f(x)在點x=x_0連續(xù)

4、是f(x)在點x=x_0可導的條件。三、計算題1. 求f(x)=x/x , phi(x)=|x|/x當x->0時的左、右極限，并說明它們在x->0時的極限是否存在。2. 求微分方程(dy)/(dx)+2xy=xeA(-xA2)的通解3. 設 z=lntan(y/x)，求 dz4.i ntxl n(1+xA2)dx5.求定積分 int_0A(1/2)1/(sqrt(1-xA2)A3)dx四、計算題二1. 已知 z=f(xy,x+y),求(de|A2z)/(delxA2),(de|A2z)/(delyA2)2. 求 in tin t_(D)cos(x+y)dxdy,D 由 y=O,y=

5、x,x=pi 所圍3. 設 y=2arctan(sqrt(x/(1-x)，求 y'五、應用題1.設某商品日產(chǎn)量是x個單位時，總費用F(x)的變化率為f(x)=0.2x+5(元仲位), 且已知F(0)=0,求(1)總費用F(x)(2)若銷售單價是25元，求總利潤(3)日產(chǎn)量為多 少時，才能獲得最大禾 潤 When you are old and grey and full of sleep,And nodding by the fire, take dow n this book,And slowly read, and dream of the soft lookYour eyes h

6、ad on ce, and of their shadows deep;How many loved your mome nts of glad grace,And loved your beauty with love false or true,But one man loved the pilgrim soul in you,And loved the sorrows of your cha nging face;And bending dow n beside the glow ing bars,Murmur, a little sadly, how love fledAnd pace

7、d upon the mountains overheadAnd hid his face amid a crowd of stars.The furthest dista nee in the worldIs not betwee n life and deathBut whe n I sta nd in front of youYet you don't know thatI love you.The furthest dista nee in the worldIs not whe n I sta nd in front of youYet you can't see my loveBut whe n un doubtedly knowing the love from bothYet cannot be together.The furthest dista nee in the worldIs not being apart while being in loveBut whe n I pla inly cannot resist the year ningYet prete nding you have n ever bee n in my heart.The furthest dista nee in the worldIs not