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Proof In parts (a) - (h), prove the property for
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Chapter 15 Solutions
Calculus
- F = (x² - y)i + + (4z)j + (x²)k Find the curl (curl calculation) of the vector field?arrow_forwardNonearrow_forwardMatch the vector fields: ? curl(F)=0 ? curl(F)=2 V 2. div(F)=0, ? curl(F)=0 ? V 3. div(F)=-1, 1. div(F)=4, ? curl(F)=1 V 4. div(F)=-2, V 5. div(F)=-2, curl(F)=-1 ? curl(F)=3 6. div(F)=2, A D B E C Farrow_forward
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- Sketch representative vectors for the vector field by sketching its scalar field.F(x,y) = -(1/2)yi + (1/5)xj; c = 1, 2*Note: c=1 and c=2 are level surface curves.Make one sketch using representative vectors for both c=1 and c=2, and make second sketch of the vector field. Please describe the difference between a scalar field and a vector field.Please give a detailed answer, noting any steps or formulas used.arrow_forwardProve the two Scalar Multiple Rules for vector functions.arrow_forwardA net is dipped in a river. Determine the flow rate of water across the net if the velocity vector field for the river is given by v=(x-y,z+y+7,z2) and the net is decribed by the equation y=1-x2-z2, y20, and oriented in the positive y- direction. (Use symbolic notation and fractions where needed.)arrow_forward
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