Question

a) If f is a smooth function, then

curl(gradf) = 0 i  + 0 j  + 0 k 


False

True

b) If G is a smooth curl field, then

divG = 0
False

True

Answer 1

I'm feeling that they are true but I'm not 100% sure

Answer 2

@dan815 are both true because divG = div(curlF)=0?

Answer 3

define smooth

Answer 4

curl(grad(f)) is always zero

Answer 5

or many its not for "non smooth" functions

Answer 6

also ya divG is different u can have a curling field but also diverging at the same time

Answer 7

unless g = Curl(H)

Answer 8

then div(curl h) is always zero

Answer 9

for smooth functions

Answer 10

G is a smooth curl field for part b

Answer 11

look up def of smooth curl field

Answer 12

it means that the field has no sharp turns right?

Answer 13

would you say that "a" is true and that "b" not necessary so false?