Question

哪位数学高手能帮我做下这张高中数学微积分试卷

Answer 1

1.{x|x>1或x<-1}
2.y=lgu,u=sinx
3.2+
4.(e^x-sinx)dx
5.(-1,+无穷)
6.y=x^2(x>=0)
7.2-
8.y=2x-1
9.以一定可导
1.错
2.错
3.错
4.增区间是C,吴减区间
5-12.CDBDDCDC
1.原式=ln1+sin0+2=2
2.题目的分母一个是2x^2+3x+1吧
(x^3+1)/(2x^2+3x+1)=(x+1)(x^2-x+1)/(x+1)(2x+1)=(x^2-x+1)/(2x+1)
原式=(1-1+1)/(2+1)=1/3
3.原式=2x^3/3+3x^2/2+x+C
4.原式=0
5.原式=无穷
6.(x-3)/(x^2-9)=1/(x+3),原式=1/6
7.看不清趋向于什么
8.[1-2/(x+1)]^(x)=[1-2/(x+1)]^[(x+1)/(-2)](-2x)/(x+1)
原式=e^(-2)
1.原式=(4/5)x^(5/2)
2.原式=∫lnxd(x^2/2)=x^2*lnx/2-∫(x/2)dx=x^2*lnx/2-x^2/4+C
3.∫(4+2x)dx=x^2+4x+C,原式=1+4-0=5
4.∫xcosxdx=∫xdsinx=xsinx-∫sinxdx=xsinx+cosx+C,原式=-1-1=-2
5.∫(cosx-e^x+1/x)dx=sinx-e^x+lnx+C,原式=sin2-e^2+ln2-sin1+e
6.原式=∫[3-3/(1+x^2)]dx=3x-3arctanx+C
7.原式=∫e^(x^2)d(x^2)/2=e^(x^2)/2+C
8.∫(x-2)dx=x^2/2-2x+C,原式=9/2-6-0=-3/2
9.∫xlnxdx=x^2*lnx/2-x^2/4+C,原式=2ln2-1-(0-1/4)=2ln2-3/4
1.y'=2x-(2/3)x^(-1/3)
2.y'=ln3*3^x
3.y'=1+1/x
4.y'=-1/根号(2x-x^2)
5.y'=12x^2+e^x-sinx
6.dy=(-2x)e^(-x^2)dx
7.2x+y'/y+cosy*y'=0,y'=2xy/(ycosy+1)
1.f'(x)=1-x^(1/3),令f'(x)=0,x=1
所以f(x)在(-无穷,1)单调增,在(1,+无穷)上单调减，极大值=1-3/2=-1/2(x=1时)
2.f(0-)=2,f(0+)=f(0)=k,要使连续,k=2
3.L'(x)=2-0.002x,令L'(x)=0，x=1000
所以L(x)在(0,1000)单调增,在(1000,+无穷)上单调减
所以最大值=500+2000-1000=1500(x=1000时)
4.L(P)=PQ-C(Q)=1000P-100P^2-5(1000-100P)-200=-100P^2+1500P-5200
L'(P)=-200P+1500=0,P=7.5
所以L(P)在(0,7.5)单调增,在(7.5,+无穷)上单调减
所以最大值=425(P=7.5时,Q=250)