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Multivariable limit problem with cos/cos

  1. Feb 13, 2015 #1

    RJLiberator

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    1. The problem statement, all variables and given/known data
    Lim (x,y) --> (pi, 0) of (cos(x-y))/(cos(x+y))

    2. Relevant equations
    The answer is 1

    3. The attempt at a solution

    My answer is this: The function is continuous at the point in question, so we only need to plug in the values which result to be 1.

    My question here: I know this function is discontinuous when cos = pi/2 or 3pi/2. As the denominator would be 0. But because my point of interest IS continuous, this allows me to proceed in the manner that I did. Correct?
     
  2. jcsd
  3. Feb 13, 2015 #2

    Dick

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    Correct. f/g is continuous if f and g are continuous and g is not 0.
     
  4. Feb 13, 2015 #3

    RJLiberator

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    Excellent. Thank you for the definition.
     
  5. Feb 13, 2015 #4

    Dick

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    It's not a definition, it's a theorem. But you are welcome.
     
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