== Consider the plane curve defined by the parametric equations x = x(t) and y =...

 

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== Consider the plane curve defined by the parametric equations x = x(t) and y = y(t). Suppose that x' (t) and y' (t) exist, and assume that x' (t) = 0. Then the derivative + is given by dy dy/dt_y' (t) = = dx dx/dt x' (t) dy == Consider the plane curve defined by the parametric equations x = x(t) and y = y(t). Suppose that x' (t) and y' (t) exist, and assume that x' (t) = 0. Then the derivative + is given by dy dy/dt_y' (t) = = dx dx/dt x' (t) dy

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Answer Analyzing the spectrum of the Laplace operator on a compact Riemannian manifold involves studying the eigenvalues and eigenfunctions of the Lap... View the full answer