1.求参量方程{x=a(cost+tsint),y=a(sint-tcost)}的二阶导数d^2y/dx^2
1个回答

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

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