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Thread: Calculus III help

  1. #1
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    Calculus III help

    Here are some questions of Cylindrical and Spherical coordinates :
    Kindly help me with the approach that I shall use to solve these questions , because I'm getting no idea.
    I shall be very thankful to you.Calculus III help-2.png
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  2. #2
    MHF Contributor

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    Re: Calculus III help

    Thankful for what? For doing your homework for you? You have shown no work of your own. Are you saying you do not know what "cylindrical coordinates" are?

    Do you know that $x^2+ y^2\le 16$ is the circle in the xy-plane with center at (0, 0) and radius 4? If that were in a three dimensional xyz- coordinate system, it would describe a cylinder with the z-axis as central axis and radius 4.

    $r\le 4$, $0\le \theta\le \pi/4$, in cylindrical coordinates, describe an eighth of a cylinder of radius 2 with central axis along the z-axis. That is because $r\e 4$ is the circle, in the xy-plane, with radius 2 while $0\le \theta\le \pi/4$ ($\pi/4 radians is 45 degrees) is 1/8 th of that circle. There is no z in the equation so there is no restriction on z- z can be anything.

    Next time you post a problem here, please do as much of it as you can or at least tell us what you do understand about the problem so we will know what hints you need.
    Thanks from sakonpure6
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