Math  /  Calculus

Question40. Let F(x,y,z)=3x2yi+(x3+y3)j\mathbf{F}(x, y, z)=3 x^{2} y \mathbf{i}+\left(x^{3}+y^{3}\right) \mathbf{j}. (a) Verify that curl F=0\mathbf{F}=\mathbf{0}. (b) Find a function ff such that F=f\mathbf{F}=\nabla f. (Techniques for constructing ff in general are given in Chapter The one in this problem should be sought by trial and error. 1

Studdy Solution
The curl of F\mathbf{F} is indeed 0\mathbf{0}, and the potential function is f(x,y,z)=x3y+14y4+Cf(x, y, z) = x^3y + \frac{1}{4}y^4 + C.

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