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

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

anonymous · Answer

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

anonymous · Answer

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

dan815 · Answer

define smooth

dan815 · Answer

curl(grad(f)) is always zero

dan815 · Answer

or many its not for  "non smooth" functions

dan815 · Answer

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

dan815 · Answer

unless g = Curl(H)

dan815 · Answer

then div(curl h) is always zero

dan815 · Answer

for smooth functions

anonymous · Answer

G is a smooth curl field for part b

dan815 · Answer

look up def of smooth curl field

anonymous · Answer

it means that the field has no sharp turns right?

anonymous · Answer

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