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Smooth curves

  1. May 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Determine where r(t) is a smooth curve for -pi <t<pi
    R(t)= (x(t),y(t))=(4sin^3(t), 4cos^3(t))

    2. Relevant equations



    3. The attempt at a solution

    To be honest I have no idea where to start. I know what a smooth function is but my understanding is that the sin(t) and cos(t) functions over all of t are smooth. No corners.
    Any starting help would be appreciated.
     
  2. jcsd
  3. May 3, 2014 #2

    HallsofIvy

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    Yes, but you are NOT asked if sine and cosine are smooth- you are asked if F is smooth. What happens if the denominator of a fraction goes to 0? What fraction is involved here?
     
  4. May 3, 2014 #3
    The function is not continuous at that particular point that makes the denominator go to zero.
    Perhaps we could rewrite in the complex plane?
     
  5. May 3, 2014 #4

    HallsofIvy

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    No, it is not necessary to work with the complex plane. What is the definition of "smooth curve"?
     
  6. May 4, 2014 #5

    LCKurtz

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    As someone on mathstackexchange said, a smooth curve is a curve with no stubble, like this: :bugeye:
     

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    Last edited: May 4, 2014
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