Question

简单的微积分题目（英文版）,80分.

Answer 1

1.e^x-1>0 e^x>1 x>0

2.a)f(-x) = sin(-4x) cos(-x) = -sin4xcosx = -f(x) is odd

b) is periodic.The period is 3π/4.

3.a) -1

b){ x^2/(1 - x^2)^(3/2) + 1/Sqrt[1 - x^2] }/ 4cos2x 连续两次求导 = 1/4

4.如图

5.

6.f' = (E^(2 x) Cos[x])/(1 + x^2) - (2 E^(2 x) x Sin[x])/(1 + x^2)^2 + (

2 E^(2 x) Sin[x])/(1 + x^2)

7.lny=cos2x lnx

1/y * y' = 1/x * cos2x - 2sin2x lnx

y'=x^Cos[2 x] (Cos[2 x]/x - 2 ln[x] Sin[2 x])

8.4+2xy^3+3y^2x^2 y' +e^(ysinx) * (y'sinx + ycosx) = 0

y'= - ( 2xy^3 +4 +e^(ysinx)*ycosx) / (e^(ysinx)*sinx + 3x^2y^2)