Let f, g be scalar functions, i be a vector function, and assuming sufficient differentiability. Then one of the following is not correct: a) div (fở) = fdiv (v) + Vf · ở b) div (fVg) = fv²g + Vf· Vg c) curl (Vf) = 0 d) div (curl v) = 0 e) curl (fi) = Vf x ỉ - fcurl (v)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let f,g be scalar functions, v be a vector function, and assuming
sufficient differentiability. Then one of the following is not
correct:
a) div (fv) = fdiv (3) + Vf · v
b) div (fVg) = ƒV²g+Vf •Vg
c) curl (Vf) = 0
d) div (curl 3) = 0
e) curl (fi) = Vf × ở – fcurl (7)
Transcribed Image Text:Let f,g be scalar functions, v be a vector function, and assuming sufficient differentiability. Then one of the following is not correct: a) div (fv) = fdiv (3) + Vf · v b) div (fVg) = ƒV²g+Vf •Vg c) curl (Vf) = 0 d) div (curl 3) = 0 e) curl (fi) = Vf × ở – fcurl (7)
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