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Calculus

Find the slope of the tangent line to the graph of the polar equation at the point specified by the value of πœƒ.
r = 1/πœƒ
πœƒ = πœ‹

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  1. dy/dx = (dr/dπœƒ) / (dx/dπœƒ) = (r' sinπœƒ + r cosπœƒ) / (r' cosπœƒ - r sinπœƒ)
    = (-sinπœƒ/πœƒ^2 + cosπœƒ/πœƒ) / (-cosπœƒ/πœƒ^2 - sinπœƒ/πœƒ)
    = (-sinπœƒ + r cosπœƒ)/(-cosπœƒ - r sinπœƒ) if πœƒβ‰ 0
    at πœƒ=πœ‹, that means
    dy/dx = -πœ‹

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    oobleck
  2. oops. did you catch my typo?

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    oobleck

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