=-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.