文档介绍：limx→-1x+1x2+1=( )
A. 0
→0时,sin3x是2x的()
A. 低阶无穷小量
C. 同阶但不等价无穷小量
(x)= x+1,x<0,在x=0处()
x2, x≥0
(x)=xeπ2,则f'(x)=()
A.(1+x)eπ2 B. (12+x)eπ2 C. (1+x2)eπ2 D. (1+2x)eπ2
(x)=x4-4x的单调增区间的是()
A.(-∞,+∞) B. (-∞,0) C.(-1,1) D. (1,+∞)
(x)在区间-3,3上连续,则-11f(3x)dx=( )
-33f(t)dt C. 13-11f(t)dt -33f(t)dt
7.(x-2+sinx)dx=( )
A. -2x-1+cosx+c B. -2x-3+cosx+c
C. -x-33-cosx+c D. –x-1-cosx+c
(x)=0x(t-1)dt,则f“(x)=( )
A.-1
=xy,则∂z∂x=( )
-1 B. yxy+1 C. yxlnx D. xy
=cos(xy),∂2y∂x2=()
(xy) (xy) C.-y2sin(xy) D.- y2cos(xy)
→0sin1x= . 0
→∞(1-2x)x3= . e-23
=ln(4x-x2),则y'(1)= . 23
=x+sinx,则dy= . (1+cosx)dx
=x32+e-x,则y”= . 34x-12+e-x
(x)dx=cos(lnx)+C,则fx= . - sin(lnx)x
17.-11xxdx= . 0
(xlnx)= . xlnx+C
=x2,直线x=1及x轴所围成的平面有界图形的面积S= . 13
=eyx,则∂z∂x|(1,1)= . -e
→1ex-elnx
limx→1ex-elnx=limx→1ex1x
=e
=cos(x2+1),求y'.
y'=cos(x2+1)'
=-sin(x2+1)∙(x2+1)'
=-2xsin(x2+1)
+x2dx
x4+x2dx=1214+x2d(4+x2)
=12ln(4+x2)+C
0 4fxdx,其中 fx=x, &x<1 11+x, &x≥1
0 4fxdx= 01xdx+ 0111+xdx
=x22|10+ln(1+x)|41
=12+ln52
(x)是连续函数,且 0xf(t)e-tdt=x,求 01f(x)dx.
等式两边对x求导,得
f(x)e-x=1
f(x)=ex
01f(x)dx= 01exdx
=ex|10
=e-1