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Continuity, proving that sin(x)sin(1/x) is continuous at 0.

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Define f(x)=sin(x)sin(1/x) if x does not =0, and 0 when x=0.

    Have to prove that f(x) is continuous at 0.

    2. Relevant equations

    We can use the definition of continuity to prove this, I believe.

    3. The attempt at a solution

    I know from previous homework assignments that sin(x) is continuous at 0, but sin(1/x) is not. Is there a way I can use this knowledge to help me solve this problem, or do I need to start from scratch? If I need to start from scratch, do I apply the definition of continuity?
  2. jcsd
  3. May 17, 2010 #2


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    Science Advisor

    Apply the definition of continuity, and think about what these functions do as they approach zero. While sin(1/x) oscillates wildly, it remains bounded. So what is the limit of your function as x->0?
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