Question

Consider the vector field ?(?,?,?)=(3?+3?)?+(4?+3?)?+(4?+3?)?. a) Find a function ? such that ?=∇? and ?(0,0,0)=0. ?(?,?,?)=  ...

Consider the vector field ?(?,?,?)=(3?+3?)?+(4?+3?)?+(4?+3?)?. a) Find a function ? such that ?=∇? and ?(0,0,0)=0. ?(?,?,?)=  

b) Suppose C is any curve from (0,0,0) to (1,1,1). Use part a) to compute the line integral ∫C ?⋅??

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the vector field F= <ey+ycosx , xey+sinx> . a) are the conditions for this field...
Consider the vector field F= <ey+ycosx , xey+sinx> . a) are the conditions for this field to be conservative satisfied? ; b) If they are, find a potential V ; c) Compute the line integral of this field for the following trajectory C : Straight line from (0 , - 1) to (1 , 0) , followed by the curve from (1 , 0) to (2 , 1), followed by the straight line from (2 , 1) to (1 ,...
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.
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the...
Consider the vector field F = <2 x y^3 , 3 x^2 y^2+sin y>. Compute the line integral of this vector field along the quarter-circle, center at the origin, above the x axis, going from the point (1 , 0) to the point (0 , 1). HINT: Is there a potential?
Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉 (a)...
Consider the vector force field given by F⃗ = 〈2x + y, 3y + x〉 (a) Let C1 be the straight line segment from (2, 0) to (−2, 0). Directly compute ∫ C1 F⃗ · d⃗r (Do not use Green’s Theorem or the Fundamental Theorem of Line Integration) (b) Is the vector field F⃗ conservative? If it is not conservative, explain why. If it is conservative, find its potential function f(x, y) Let C2 be the arc of the half-circle...
2. Consider the line integral I C F · d r, where the vector field F...
2. Consider the line integral I C F · d r, where the vector field F = x(cos(x 2 ) + y)i + 2y 3 (e y sin3 y + x 3/2 )j and C is the closed curve in the first quadrant consisting of the curve y = 1 − x 3 and the coordinate axes x = 0 and y = 0, taken anticlockwise. (a) Use Green’s theorem to express the line integral in terms of a double...
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
onsider the function ?(?,?)=(3?2 +6??−2?2)?+(3?2 −4??+3?2)?. a) Without finding a potential function, show how you can...
onsider the function ?(?,?)=(3?2 +6??−2?2)?+(3?2 −4??+3?2)?. a) Without finding a potential function, show how you can tell that that any line integral ∫ ?(?, ?) ∙ ?? ? Page 5 along any curve C is independent of the path between the endpoints of C for the function F given above. b) Find the potential function associated with the F given above. c) Use that potential function to evaluate the line integral of F along the curve C which is the...
find the line integral (total work) of the vector forces field f over the curve c...
find the line integral (total work) of the vector forces field f over the curve c given below. f=xy,xz,y=xyi+xzj+yk. c=straight line from point (0,1,1) to point (2,1,3)
(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. A trail of ants on a silo is described by the helix ?: ?⃗(?) =...
1. A trail of ants on a silo is described by the helix ?: ?⃗(?) = (cos ?)?̂+ (sin ?)?̂+ (3?)?̂ , for 0 ≤ ? ≤ 4?. The “linear ant density” along the trail is given by : ?(?, ?, ?) = 5? 2 + 5? 2 + 12? ???? ? . Evaluate the line integral : ∫ ?(?, ?, ?) ? ?? , and describe what this value represents. 2. Given the function: ?(?, ?) = 2?? −...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT