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Many quantities depend on more than one variable: the amount of food grown depends on the amount of rain and the amount of fertilizer used: the rate of a chemical reaction depends on the temperature and the pressure of the environment in which it proceeds: the strength of the gravitational attraction between two bodies depends on their masses and their distance apart: and the rate of fallout from a volcanic explosion depends on the distance from the volcano and the time since the explosion.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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central vector field, curl test, find parametric equations, circulation density, nonzero circulation, parameter rectangle, contour diagram, local linearity, curl field, oriented counterclockwise, parameterized surfaces, flux integral, global extrema, divergence test, area vector, local linearization, geometric definition, velocity vector field, particle whose motion, parameterized curves, curve parameterized, coordinate definition, oriented clockwise, algebraic definition, second derivative test
Key Phrases - Capitalized Phrases (CAPs):
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Divergence Theorem, New York, Exercises In Exercises, Fundamental Theorem of Calculus, Challenge Problems, Solution Let, Use Problem, Exercises For Exercises, Coulomb's Law, Kepler's Second Law, Solution First, Conservation of Energy, Half Dome, Interpretation of the Double Integral, Solution Figure
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