If F:R3→R3 and f:R3→R are C2 functions, then show that ∇⋅(∇×F)=0, and ∇×∇f=0. Question 15 Let F:R3→R3 where F(x,y,z)= (3
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If F:R3→R3 and f:R3→R are C2 functions, then show that ∇⋅(∇×F)=0, and ∇×∇f=0. Question 15 Let F:R3→R3 where F(x,y,z)= (3
If F:R3→R3 and f:R3→R are C2 functions, then show that ∇⋅(∇×F)=0, and ∇×∇f=0. Question 15 Let F:R3→R3 where F(x,y,z)= (3x2y,x3+y3,1). Find a scalar-valued function f:R3→R such that F=∇f and f(0,0,0)=1.
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