Web(I seem to get answers that indicate that the vector field in question is not conservative, but it should be.) The question is listed below: Show that the vector field F ( x, y, z) = ( 2 x + y) i + ( z cos ( y z) + x) j + y cos ( y z) k is conservative and determine a potential function. calculus Share Cite Follow edited Mar 5, 2024 at 15:54 BigM WebNov 16, 2024 · Section 16.6 : Conservative Vector Fields For problems 1 – 3 determine if the vector field is conservative. →F = (x3 −4xy2 +2)→i +(6x −7y +x3y3)→j F → = ( x 3 − 4 x y 2 + 2) i → + ( 6 x − 7 y + x 3 y 3) j → Solution →F = (2xsin(2y)−3y2)→i +(2 −6xy +2x2cos(2y))→j F → = ( 2 x sin ( 2 y) − 3 y 2) i → + ( 2 − 6 x y + 2 x 2 cos ( 2 y)) j → …

Conservative vector fields (article) Khan Academy

Web(1 point) Determine if the vector field F (x, y, z) = (72)i + (2xyz)j + (3xy ?)k is conservative curl (F) Σ Therefore F A. In contervative OB. Is not conservative It F is conservative find a function such that F = VS. WebDetermine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇ f . (If the vector field is not conservative, enter DNE.) iowa chop brine

Determine if the vector field is conservative or not

WebDec 18, 2024 · Find the conservative vector field for the potential function \(f(x,y)=5x^2+3xy+10y^2.\) Answer \(\vecs{F}(x,y)=(10x+3y)\,\mathbf{\hat i}+(3x+20y)\,\mathbf{\hat j}\) For the following exercises, determine whether the vector field is conservative and, if so, find a potential function. WebIf a vector field is not path-independent, we call it path-dependent (or non-conservative). The vector field F ( x, y) = ( y, − x) is an example of a path-dependent vector field. This vector field represents clockwise … WebOct 18, 2015 · If one can find, for example, an smooth, oriented loop $\gamma$ such that at every point of $\gamma$ the unit tangent vector makes a zero, acute, or right angle, and … oofy roblox group