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Posted: **Thu Jul 14, 2022 4:08 pm**

: 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 1 (75.43 KiB) Viewed 33 times

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.