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Mathematics, 26.10.2019 03:43 miguelmike2895

Show that if the vector field f = pi + qj + rk is conservative and p, q, r have continuous first-order partial derivatives, then the following is true. βˆ‚p βˆ‚y = βˆ‚q βˆ‚x βˆ‚p βˆ‚z = βˆ‚r βˆ‚x βˆ‚q βˆ‚z = βˆ‚r βˆ‚y . since f is conservative, there exists a function f such that f = βˆ‡f, that is, p, q, and r are defined as follows. (enter your answers in the form fx, fy, fz.) p = q = r = since p, q, and r have continuous first order partial derivatives, says that βˆ‚p/βˆ‚y = fxy = fyx = βˆ‚q/βˆ‚x, βˆ‚p/βˆ‚z = fxz = fzx = βˆ‚r/βˆ‚x, and βˆ‚q/βˆ‚z = fyz = fzy = βˆ‚r/βˆ‚y.

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