solutions to uniform final exam for calculus iii math 2421 fall 2007 1 suppose f and g are vector elds and f and g are scalar functions assume all partial ...
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...Solutions to uniform final exam for calculus iii math fall suppose f and g are vector elds scalar functions assume all partial derivatives exist which one of these expressions is an illegal operation in example we can only dot product two valued since r a function cannot it with the deloperator nd divergence correct answer c force has components h i pounds this moves object feet straight line if angle separation between displacement then how much work does accomplish pq kfk cos q ft lbs lb units b z x y s t u expression below equivalent there paths from down wehave diagrams surfaces solids follow usual display conven tions positive axis comes out paper points right origin basically located at center cube circular cone xy plane p must be nonnegative surface reside except now square both sides gives us upper lower cones wealready know that choose ii half ellipsoid hyperbolic paraboloid saddle shape vi solid region cylinders andx let simple closed bounds hemisphere use appropriate formula...