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    divergence and curl of the given vector field

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    Calculate the divergence and curl of the given vector field F.

    F(x,y,z)=3xi-2yj-4zk

    F(x,y,z)=(x^2 e^(-z) )i+(y^3 ln⁡〖x)〗 j+(z cosh y)k

    Evaluate ∫_C▒〖P(x,y)dx+Q(x,y)dy〗

    P(x,y)=xy, Q(x,y)=x+y; C is part of the graph of y = x² from (-1,1) to (2,4)

    Show that the given line integral is independent of path in the entire xy-plane, then calculate the value of the line integral.

    ∫_((0,0))^((1,1))▒〖(2x-3y)dx+(2y-3x)dy〗

    ∫_((0,0))^((1,-1))▒〖(e^y 〗+ye^x)dx+(e^x+xe^y )dy

    © BrainMass Inc. brainmass.com March 4, 2021, 10:23 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/divergence-curl-given-vector-field-327040

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    Calculate the divergence and curl of the given vector field F.

    1.
    Divergence:
    We have
    Curl:
    We have
    Hence
    2.
    Divergence:
    We have
    Curl:
    We have ...

    Solution Summary

    The expert calculates the divergence and curl of the given vector field F.

    $2.19

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