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angle antiderivative approximately assume axis calculate center of gravity Chain Rule circle compute conic section Consequently constant converges curve cylinder deﬁned deﬁnition denote determine differential equation distance diverges domain of f ellipse evaluate Example 1 Let exists f and g f is continuous feet ﬁnd ﬁrst follows function f given grad graph of f Green's Theorem Hint hyperbola integral Intermediate Value Theorem length Let f Let f(x lim f(x limit line integral maximum value Mean Value Theorem nonnegative object parabola parallelepiped parametrized partial derivatives perpendicular polar coordinates polynomial power series prove radius real numbers rectangle relative extreme value Riemann sum satisﬁes Section Show that f simple region sinx sketch the graph solid region bounded Solution Solutlon Suppose surface area tangent line Taylor series triangle value of f Value Theorem variables vector-valued function velocity vertical volume xy plane