人工智能教程 – 数学基础课程1.1 – 数学分析(一) 28 31 参数方程极坐标不定型和洛必达法则

参数方程弧长和表面积 ​​ ​​ 斜边长度平方 (hypotenuse) (ΔS)2=(Δx)2+(Δy)2(\Delta S)^2 = (\Delta x)^2 +(\Delta y)^2(ΔS)2=(Δx)2+(Δy)2 (dS)2=(dx)2+(dy)2(dS)^2 = (d x)^2 +(d y)^2(dS)2=(dx)2+(dy)2 simplify: dS2=dx2+dy2dS^2 = d x^2 +d y^2dS2=dx2+dy2 ds=1+(dy/dx)2dxds = \sqrt{ 1+(dy/dx)^2}dxds=1+(dy/dx)2​dx Arclength:(total