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3. Let y be a continuously differentiable vector field defined on all of R" and which satisfies du Ouj vi,je (1, . . ..n). (1) Define f: R" -> R by f(x) := fo x . v(tx) dt. Prove that Vf(x) = (z). Remarks. f is called a scalar potential of v. The curl of a vector field was defined as a skewsymmetric matrix in Question 5 of Supplementary Examples Sheet 8. Observe that the curl of a vector field vanishes precisely if it satisfies (1)