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Homework Help: Study the continuity of this function

  1. Nov 24, 2012 #1
    1. The problem statement, all variables and given/known data

    f(x) = [x^2]sinπx, x ∈ R, being [x] the integer part of x

    2. Relevant equations

    3. The attempt at a solution

    I'd say it's trivially continuos on all R, because it's the product of two continuos functions: y: = [x^2] and g: = sinπx.
    However, being part of my analysis class homework (always a bit tricky to solve), it seems a bit too easy to me. So, i thought there might be something strange I haven't noticed. Or is my reasoning just correct?
    thanks in advance!!
  2. jcsd
  3. Nov 24, 2012 #2


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    Science Advisor
    Homework Helper

    x^2 is continuous. The integer part of x^2 is not continuous.
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