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 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"
(1 point) For each of the following vector fields F , decide
whether it is conservative...
(1 point) 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)=(10x+7y)i+(7x+10y)j f(x,y)= 10 B. F(x,y)=5yi+6xj
f(x,y)= N C. F(x,y,z)=5xi+6yj+k f(x,y,z)= D.
F(x,y)=(5siny)i+(14y+5xcosy)j f(x,y)= E.
F(x,y,z)=5x2i+7y2j+5z2k
2. Is the vector field F = < z cos(y), −xz sin(y), x
cos(y)> conservative? Why...
2. Is the vector field F = < z cos(y), −xz sin(y), x
cos(y)> conservative? Why or why not? If F is conservative, then
find its potential function.
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
.
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
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y>
conservative?
(b) If...
(a) Is the vector field F = <e^(−x) cos y, e^(−x) sin y>
conservative?
(b) If so, find the associated potential function φ.
(c) Evaluate Integral C F*dr, where C is the straight line path
from (0, 0) to (2π, 2π).
(d) Write the expression for the line integral as a single
integral without using the fundamental theorem of calculus.
(1 point) In each case, if the vector field is conservative,
give the potential function whose...
(1 point) In each case, if the vector field is conservative,
give the potential function whose value at the origin is zero;
otherwise answer NA.
(1) 〈4yz(xyz)^3,4xz(xyz)^3,4xy(xyz)^3〉
(2) 〈−ysin(x)z,zcos(x),ycos(x)〉
(3) 〈y,x+z,y〉
(4) 〈−y,x〉
(5) 〈3y−3z,3z,−(3y+3x)
(6) 〈exp(x)cos(y),−(exp(x))sin(y),4(z^3)〉
Please show all steps when finding potential
functions.
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
Consider the vector field F(x,y,z)=〈−3y,−3x,−4z〉. Find a
potential function f(x,y,z) for F which satisfies f(0,0,0)=0.
Consider the vector field F(x,y,z)=〈−3y,−3x,−4z〉. Find a
potential function f(x,y,z) for F which satisfies f(0,0,0)=0.