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Evaluating a Line
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Multivariable Calculus
- Application of Green's theorem Assume that u and u are continuously differentiable functions. Using Green's theorem, prove that JS D Ur Vy dA= u dv, where D is some domain enclosed by a simple closed curve C with positive orientation.arrow_forwardApplication of Green's theorem Assume that u and v are continuously differentiable functions. Using Green's theorem, prove that SS'S D Ux Vx |u₁|dA= udv, C Wy Vy where D is some domain enclosed by a simple closed curve C with positive orientation.arrow_forwardUsing Green's Theorem, find the outward flux of F across the closed curve C.F = (-5x + 2y) i + (6x - 9y) j; C is the region bounded above by y = -5x 2 + 250 and below by y=5x2 in the first quadrantarrow_forward
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- Consider the vector-valued function r(t) = 3t2i + (t − 1)j + tk. Write a vector-valued function u(t) that is the specified transformation of r. A horizontal translation one unit in the direction of the positive x-axisarrow_forwardConsider the vector-valued function r(t) = 3t2i + (t − 1)j + tk. Write a vector-valued function u(t) that is the specified transformation of r.A vertical translation two units upwardarrow_forwardCalculus Let T be a linear transformation from P into R such that T(p)=01p(x)dx. Find (a) T(2+3x2), (b) T(x3x5), and (c) T(6+4x).arrow_forward
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