Decide if the given vector field is the gradient of a

Last updated: 6/21/2023

Decide if the given vector field is the gradient of a function f If so find f Remember to use absolute values where appropriate If an ane does not exist enter DNE 1 1 1 f x y z In x In y ln z x c If not explain why not 1 7 is the gradient of a function y 1 1 is not the gradient of a function because the curl of the field is not equal to zero xyz 1 1 k is not the gradient of a function because the field is not path independent xyz 1 1 is not the gradient of a function because the field has no potential function X y 1 1 4 m is not the gradient of a function because 7 7 dre 7 dr 0 for every c closed curve C