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x=sint,y=tsint+cost,求d^2y/dx^2It=π/4,急等啊
题目详情
x=sint,y=tsint+cost,求d^2y/dx^2It=π/4,急等啊
▼优质解答
答案和解析
dx/dt=cost
dy/dt=sint+tcost-sint=tcost
y'=dy/dx=(dy/dt)/(dx/dt)=t
y"=d^2y/dx^2=d(y')/dx=d(y')/dt/(dx/dt)=1/cost
当t=π/4时,y"=1/cos(π/4)=√2
dy/dt=sint+tcost-sint=tcost
y'=dy/dx=(dy/dt)/(dx/dt)=t
y"=d^2y/dx^2=d(y')/dx=d(y')/dt/(dx/dt)=1/cost
当t=π/4时,y"=1/cos(π/4)=√2
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