求教,这道高数题目怎么解?看上去好像会的样子,可是做起来发现dy⼀dx为无穷,答案还是y=2+ln2(x-1)

2025-05-07 13:20:28
推荐回答(2个)
回答1:

(1)先求t=0处的切点坐标
x(0)=1+0+0^2=1
y(0)^(-0)*e^y(0)=e^2,y(0)=2
所以t=0处的切点坐标为(1,2)
(2)再求t=0处的切线斜率
dx/dt=1+2t
lny^(-t)+lne^y=lne^2,-t*lny+y=2,-lny-(t/y)*dy/dt+dy/dt=0
dy/dt=lny/(1-t/y)=ylny/(y-t)
dy/dx=(dy/dt)/(dx/dt)=ylny/(y-t)(1+2t)
dy/dx|(t=0)=y(0)lny(0)/y(0)=ln2
(3)所求切线方程为:y-2=ln2*(x-1)
y=2+ln2*(x-1)

回答2: