Question

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.

  1. b) Find the potential function associated with the F given above.

  2. c) Use that potential function to evaluate the line integral of F along the curve C which is the

    part of the ellipse ?2 + ?2 = 1 which lies in the first quadrant and goes from the point on the

    x-axis to the point on the y-axis.

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
Show that for F(x, y) = 〈6x2y − 4, 2x3 − 4y3 + 4〉, the line...
Show that for F(x, y) = 〈6x2y − 4, 2x3 − 4y3 + 4〉, the line integral ∫ C F(x, y) · dr is independent of path. Then, evaluate the line integral for any curve C with initial point at (−1, 3) and terminal point at (3, 4).
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?
Use the rectangles to approximate the area of the region. (Round your answer to three decimal...
Use the rectangles to approximate the area of the region. (Round your answer to three decimal places.) The x y-coordinate plane is given. There is 1 curve, a shaded region, and 4 rectangles on the graph. The curve enters the window in the first quadrant, goes down and right becoming less steep, passes through the point (1, 5), passes through the point (5, 1), and exits the window almost horizontally above the x-axis. The region below the curve, above the...
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?? −...
The function f(x, y) = x^−2 y^3 is a potential for a vector field F. Use...
The function f(x, y) = x^−2 y^3 is a potential for a vector field F. Use this to evaluate ∫ C F · dr where C is a curve from (1, 1) to (2, 2).
explain how you can tell whether g(x)=3-4x^2-x^3 has an inverse that is a function. then give...
explain how you can tell whether g(x)=3-4x^2-x^3 has an inverse that is a function. then give the coordinates of any point on the graph of the inverse.
Consider the function given byf(x, y) =((y^2−2^x)/(2x^2+y^2))^3.Show that lim(x,y)→(0,0)f(x, y)does not exist by computing the limit...
Consider the function given byf(x, y) =((y^2−2^x)/(2x^2+y^2))^3.Show that lim(x,y)→(0,0)f(x, y)does not exist by computing the limit along the positivex-axis and the positivey-axis.
Find the limits, if exists 1. lim?→−6 ?^2 − ? + 4/6 − ? = 2....
Find the limits, if exists 1. lim?→−6 ?^2 − ? + 4/6 − ? = 2. lim?→5 2? − 10 /(? − 5)(? + 3) = 3. lim?→−4 ?(?) , ?? ?(?) = { 2? + 5, ? < −1 /13 − ? 2 , ? ≥ −1 4. lim?→∞ 4?^3 − 5 /4?^2 + 3? − 1 = Part II. Find the derivative of the function. 1. ? = 12?^3 + 2?^2 − ? + 3 2. ?(?) =...
1. Answer Following Questions, Show work, clear hand writing, thank you a. Set up (i.e. DO...
1. Answer Following Questions, Show work, clear hand writing, thank you a. Set up (i.e. DO NOT SOLVE) an integral to find the volume of the solid obtained when the given region is rotated about the given axis. The region bounded by y = 2x^2 and y = 2x^3 about the line x = −1 b. get the general antiderivative of f(x) = (x^2)*(e^−x) c. Find the length of the polar curve r = 2cosθ
1. Let u(x) and v(x) be functions such that u(1)=2,u′(1)=3,v(1)=6,v′(1)=−1 If f(x)=u(x)v(x), what is f′(1). Explain...
1. Let u(x) and v(x) be functions such that u(1)=2,u′(1)=3,v(1)=6,v′(1)=−1 If f(x)=u(x)v(x), what is f′(1). Explain how you arrive at your answer. 2. If f(x) is a function such that f(5)=9 and f′(5)=−4, what is the equation of the tangent line to the graph of y=f(x) at the point x=5? Explain how you arrive at your answer. 3. Find the equation of the tangent line to the function g(x)=xx−2 at the point (3,3). Explain how you arrive at your answer....
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT