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曲线:2x-y-z=0,z=xy,在点(1,1,1)处的切线方程;
设x=t,z=ty,z=2t-y,ty=2t-y,y=2t/(1+t)
z=ty=2t²/(t+1)
的参数方程:
x=t
y=2t/(1+t);
z=2t²/(1+t)
x'=1,
y'=2/(1+t)-2t/(1+t)²=2/(1+t)²;
z'=4t/(1+t)-2t²/(1+t)²=(4t+2t²)/(1+t)²;
t=1,代入:
x'=1;
y'=1/2;
z'=3/2;
切线方程:
(x-1)/1=(y-1)/(1/2)=(z-1)/(3/2)
设x=t,z=ty,z=2t-y,ty=2t-y,y=2t/(1+t)
z=ty=2t²/(t+1)
的参数方程:
x=t
y=2t/(1+t);
z=2t²/(1+t)
x'=1,
y'=2/(1+t)-2t/(1+t)²=2/(1+t)²;
z'=4t/(1+t)-2t²/(1+t)²=(4t+2t²)/(1+t)²;
t=1,代入:
x'=1;
y'=1/2;
z'=3/2;
切线方程:
(x-1)/1=(y-1)/(1/2)=(z-1)/(3/2)
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