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/etc/nginx/nginx.conf.请问一个数学微积分问题如图,X.Y.Z的长度根据时间增长而增长.当X=4,Y=3这一瞬间时,dx/dt=dz/dt.dy/dt=k*dz/dt.求k.请写出 分析过程.
dz=√dx^2+dy^2dz/dx=√(1+y'^2)dz/dt=dx/dtdz/dx=1√(1+y'^2)=11+y'^2=1y'=0dy/dx=0y=Cx x=4,y=3 C=3/4)x=y/C x'=1/C=4/3dz/dy=√(1+x'^2)dy/dt=kdz/dtdz/dy=1/k√(1+x'^2)=1/k√[1+(4/3)^2]=1/k5/3=1/kk=3/5
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t=0的条件不全。
5/7 ,由图可知，x^2+y^2=z^2,对此式两边对时间求导，得x*x'+y*y'=z*z'.其中x'等表示对时间的倒数，把（x,y,z）=(3,4,5)带入得：3x'+4y'=5z‘；又因为dx/dt=dz/dt，所以7y'=5z'，所以k=y'/z'=5/7
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