=-2( 1-x)^ 1/2|( 1,0)

=0-(-2)

=2

Knowledge used: a basic integral, also learned in high school.

2、dx/da= 1-sina-acosa

dy/da=cosa-asina

dy/dx=(dy/da)/(dx/da)

=(cosa-asina)/( 1-Sina-acosa)

=( 1/2-√3π/6)/( 1-√3/2-π/6)

=(3-√3π)/(6-3√3-π)

Using differential knowledge

3. From both sides

e^y*y'+y+xy'=0

y'=-y/(e^y+x)

y''=[-y'(e^y+x)-(-y)(e^y*y'+ 1)](e^y+x)^2

Bring y' into and simplify:

y ' ' =(2e^y+2xy-y^2*e^y)/(e^y+x)^3

Knowledge of higher derivatives.

4, the original formula = lim [(sinx/cosx)-x]/x 2 sinx and sinx are of the same order.

= lim (1/cosx-1)/x 2 Lopida's law is used up and down.

=lim( 1/cos^2x)sinx/2x

= lim (1/cos 2x)/2 x is in the same order as sinx, which brings x=0.

= 1/2

Use the limits of knowledge.