1.求参量方程{x=a(cost+tsint),y=a(sint-tcost)}的二阶导数d^2y/dx^2
问题描述：
1.求参量方程{x=a(cost+tsint),y=a(sint-tcost)}的二阶导数d^2y/dx^2
2.求曲线y=根号下x^2-1的斜渐进线
答
dx/dt=-asint+asint+atcost=atcost
d^2x/dt^2=acost-atsint
dy/dt=acost-acost+atsint=atsint
d^2y/dt^2=asint+atcost
所以d^2y/dx^2=(d^2y/dt^2)/(d^2x/dt^2)
=(asint+atcost)/(acost-atsint)
设渐进线是y=ax+b
a=lim 根号下(x^2-1)/x=1,x趋于无穷大
b=lim (y-x),x趋于1时
=lim 根号下(x^2-1)-x=-1
所以渐进线是y=x-1