Mathematics, 17.07.2019 07:00 domjuan1456
Consider the vector field f(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)kf(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)k. a. find a function ff such that f=∇ff=∇f and f(0,0,0)=0f(0,0,0)=0. f(x, y,z)=f(x, y,z)= b. suppose c is any curve from (0,0,0)(0,0,0) to (1,1,,1,1). use part a. to compute the line integral ∫cf⋅dr∫cf⋅dr.
Answers: 1
with respect to 
![= [2(1)(1)+5(1)(1) +3(1)(1)] -[ 2(0)(0)+5(0)(0) +3(0) (0)]\\\\= (2+5+3)-0\\\\ = 10](/tpl/images/0099/2674/ff400.png)
such that
is an arbitrary constant.
is then
is any path connecting the given points)
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Consider the vector field f(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)kf(x, y,z)=(2z+5y)i+(z+5x)j+(y+2x)k. a. f...
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