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Math Help - vector calculus - vector feilds

  1. #1
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    vector calculus - vector feilds

    find the gradient vector feild ∇f of f and sketch it

    f(x,y) = sqrt(x^2 +y^2)
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  2. #2
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    Quote Originally Posted by oohaysomeone View Post
    find the gradient vector feild ∇f of f and sketch it

    f(x,y) = sqrt(x^2 +y^2)
    Do you know the definition of ∇f? Where is your impediment in applying it?
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  3. #3
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    to find the gradient, i think i have to follow this formula:

    ∇f (x,y) = (fx, fy)

    i think the first order partial derivitives will then be:

    dF/dx = (1/2) * 2x * (x^2 + y^2)^(-1/2) = x * (x^2 + y^2)^(-1/2)

    dF/dy = (1/2) * 2y * (x^2 + y^2)^(-1/2) = y * (x^2 + y^2)^(-1/2)


    is this right? what step would i take next and how would i sketch this?
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  4. #4
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    Quote Originally Posted by oohaysomeone View Post
    to find the gradient, i think i have to follow this formula:

    ∇f (x,y) = (fx, fy)

    i think the first order partial derivitives will then be:

    dF/dx = (1/2) * 2x * (x^2 + y^2)^(-1/2) = x * (x^2 + y^2)^(-1/2)

    dF/dy = (1/2) * 2y * (x^2 + y^2)^(-1/2) = y * (x^2 + y^2)^(-1/2)


    is this right? what step would i take next and how would i sketch this?
    You've more or less done it. To draw the vector field, you're probably expected to substitute values of x and y and then draw a small directed line segment at that point. I'm sure your textbook or notes will have examples.
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