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acceleration vectors calculate cartesian equations center of mass characteristic equation circle coefficients component cone Consider constant converges absolutely counterclockwise curvature curve cylinder cylindrical coordinates derivative of f determine differential equation directional derivative divergence theorem diverges double integral dr d0 dx dy dy dx evaluate field F find the area function f function f(x,y geometric series gradient vector Green's theorem Hence intersection Let us find line integral linear Maclaurin series magnitude maximum motion orthogonal parabola paraboloid parametric equations partial derivatives perpendicular polar coordinates polynomial position vector power series Problem radius region of integration scalar SELF-TEST sequence series converges sketch the region solid SOLUTIONS TO CHAPTER solve space specified sphere spherical coordinates surface area surface integral Taylor series triple integration unit normal unit vector variables vector field velocity and acceleration x-axis z-axis