这倒高数题怎么做呀,帮帮忙?
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x = arctant, y = (1/2)ln(1+t^2), t = 1 时, x = π/4, y = (1/2)ln2。
dy/dx = (dy/dt)/(dx/dt) = [t/(1+t^2)]/[1/(1+t^2)] = t
t = 1时 , 切线斜率 dy/dx = 1, 则法线斜率 k = -1,
法线方程 y = -(x-π/4) + (1/2)ln2, 即 x+y = π/4 + (1/2)ln2
dy/dx = (dy/dt)/(dx/dt) = [t/(1+t^2)]/[1/(1+t^2)] = t
t = 1时 , 切线斜率 dy/dx = 1, 则法线斜率 k = -1,
法线方程 y = -(x-π/4) + (1/2)ln2, 即 x+y = π/4 + (1/2)ln2
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