For each of the
following vector fields F , decide whether it is
conservative or not...
For each of the
following vector fields F , decide whether it is
conservative or not by computing curl F . Type in
a potential function f (that is, ∇f=F∇f=F
). If it is not conservative, type N.
A.
F(x,y)=(−10x+3y)i+(3x+10y)jF(x,y)=(−10x+3y)i+(3x+10y)j
f(x,y)=f(x,y)=
B.
F(x,y)=−5yi−4xjF(x,y)=−5yi−4xj
f(x,y)=f(x,y)=
C.
F(x,y,z)=−5xi−4yj+kF(x,y,z)=−5xi−4yj+k
f(x,y,z)=f(x,y,z)=
D.
F(x,y)=(−5siny)i+(6y−5xcosy)jF(x,y)=(−5siny)i+(6y−5xcosy)j
f(x,y)=f(x,y)=
E.
F(x,y,z)=−5x2i+3y2j+5z2kF(x,y,z)=−5x2i+3y2j+5z2k
f(x,y,z)=f(x,y,z)=
Note: Your answers should be either expressions of x, y and z
(e.g. "3xy + 2yz"), or the letter "N"
For each of the following vector fields F , decide whether it is
conservative or not...
For each of the following vector fields F , decide whether it is
conservative or not by computing curl F . Type in a potential
function f (that is, ∇f=F). If it is not conservative, type N. A.
F(x,y)=(−4x+3y)i+(3x+16y)j f(x,y)= B. F(x,y)=−2yi−1xj f(x,y)= C.
F(x,y,z)=−2xi−1yj+k f(x,y,z)= D. F(x,y)=(−2siny)i+(6y−2xcosy)j
f(x,y)= E. F(x,y,z)=−2x2i+3y2j+8z2k
For the following vector fields F , decide
whether it is conservative or not by computing...
For the following vector fields F , decide
whether it is conservative or not by computing curl
F . Type in a potential function f (that is,
∇f=F∇f=F). If it is not conservative, type N.
F(x,y,z)=−2x2i+3y2j+8z2k
Consider the vector field →F=〈3x+7y,7x+5y〉F→=〈3x+7y,7x+5y〉
Is this vector field Conservative? yes or no
If so:
Find...
Consider the vector field →F=〈3x+7y,7x+5y〉F→=〈3x+7y,7x+5y〉
Is this vector field Conservative? yes or no
If so:
Find a function ff so that →F=∇fF→=∇f
f(x,y) =_____ + K
Use your answer to evaluate ∫C→F⋅d→r∫CF→⋅dr→ along the curve C:
→r(t)=t2→i+t3→j, 0≤t≤3r→(t)=t2i→+t3j→, 0≤t≤3
Determine whether or not the vector field is conservative. If it
is conservative, find a function...
Determine whether or not the vector field is conservative. If it
is conservative, find a function f such that F = ∇f. (If the vector
field is not conservative, enter DNE.)
F(x, y, z) = 8xyi + (4x2 + 10yz)j + 5y2k
Find: f(x, y, z) =
Which of the following vector fields are conservative?
(i)
F(x, y) =
(7x6y6 +
3) i ...
Which of the following vector fields are conservative?
(i)
F(x, y) =
(7x6y6 +
3) i +
(6x7y5 +
7) j
(ii)
F(x, y) =
(6ye6x +
sin 3y) i +
(e6x +
3x cos 3y) j
(iii)
F(x, y) =
7y2e7xy i
+ (7 +
xy) e7xy j
Determine whether or not F is a conservative
vector field. If it is, find a function...
Determine whether or not F is a conservative
vector field. If it is, find a function f such that
F = ∇f. (If the vector field is not
conservative, enter DNE.)
F(x, y) = (y2 − 8x)i + 2xyj
Determine whether or not F is a conservative
vector field. If it is, find a function...
Determine whether or not F is a conservative
vector field. If it is, find a function f such that
F = ∇f. (If the vector field is not
conservative, enter DNE.)
F(x, y) = (y2 − 8x)i + 2xyj
F(x, y, z) = sin y i + (x.cos y + cos z) j – y.sinz...
F(x, y, z) = sin y i + (x.cos y + cos z) j – y.sinz k
a) Determine whether or not the vector field is
conservative.
b) If it is conservative, find the function f such that F = ∇f
.
Consider the following vector field.
F(x, y, z) =
6yz ln x i + (3x −...
Consider the following vector field.
F(x, y, z) =
6yz ln x i + (3x −
7yz) j +
xy8z3 k
(a)
Find the curl of F evaluated at the point
(5, 1, 4).
(b)
Find the divergence of F evaluated at the
point (5, 1, 4).