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Decide whether the following functions are continuous at a=0

  1. Jan 13, 2009 #1
    1. The problem statement, all variables and given/known data

    Decide whether the following functions are continuous at a=0

    2. Relevant equations

    f(x)=x^2 if x<0 and f(x)=sinx if x>=0

    3. The attempt at a solution

    I don't really understand where the 'a' comes in the functions? Some help/hints as to how to start off this question would be much appreciated.
     
  2. jcsd
  3. Jan 13, 2009 #2

    Hootenanny

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    Re: continuity

    a is simply the point under consideration. More verbosely the question could ask "Let a=0. Decide whether the following functions are continuous at x=a ...". So, you simply need to examine the continuity of the f(x) at the origin.
     
  4. Jan 13, 2009 #3
    Re: continuity

    ok, thankyou.

    So im looking at the left hand part of the parabola of x^2, which is when x<0.
    It stops at x=0, im not really sure what to say about the continuity.
     
  5. Jan 13, 2009 #4

    danago

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    Re: continuity

    Do you know the formal definition of continuity? What conditions must be met?
     
  6. Jan 13, 2009 #5

    Hootenanny

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    Re: continuity

    HINT: Looking at the question, the first thing to consider would be whether a=0 belongs to the domain of f ...
     
  7. Jan 13, 2009 #6

    HallsofIvy

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    Re: continuity

    Good point, Hootenanny, but I am wodering if the OP didn't just misstate the definition of f.
     
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