Question: 6. Consider the gradient vector field given by V(f) (x, y, z) = (4x23)i + (6x222 + ez )k. (a) Let c(t) = (sint, cost,

6. Consider the gradient vector field given by V(f) (x, y, z) = (4x23)i + (6x222 + ez )k. (a) Let c(t) = (sint, cost, 2), te [0, "]. Compute (v (f ) . ds (b) Let c(t) = (cost, sint, 2), t E [0, 27] be a parametrization of the unit circle, traversed counterclockwise. Calculate V (f) . ds Page 2 (c) (Marsden-Tromba 7.2.16) What is the value of the integral of a gradient vector field around a closed curve C? Be sure to justify your

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