Results 1 to 6 of 6

Math Help - Continuous functions

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    India
    Posts
    3

    Continuous functions

    Hi,

    I have a lot of ambiguity about understanding the concept of continuous functions.The general explanation given for a continuous function is that the point moves smoothly without a break.Then is a constant function continuous?

    let us assume,f(x)=2*X then df/dx =2 is this continuous?

    can anyone explain this to me?
    -swetha
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1291

    Re: Continuous functions

    A function is continuous if the function is defined at every point, and if the limit of the function at that point exists and is equal to the function value.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: Continuous functions

    Last edited by princeps; April 9th 2012 at 12:35 AM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,367
    Thanks
    1311

    Re: Continuous functions

    Yes, every constant function is continuous. In fact, every polynomial is continuous.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Apr 2012
    From
    India
    Posts
    3

    Re: Continuous functions

    Thankyou for your answers.so,if f(x)= constant then y=df/dx=0 =>y(x)=0 which represents the real-line.I think y is also continuous. am i right?
    -swetha
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1291

    Re: Continuous functions

    Quote Originally Posted by swethapradeepp View Post
    Thankyou for your answers.so,if f(x)= constant then y=df/dx=0 =>y(x)=0 which represents the real-line.I think y is also continuous. am i right?
    -swetha
    Yes, since a constant function is a polynomial (of degree 0) and all polynomials are continuous.

    Or to use the more precise definition, the constant function is defined at every point (and is equal to that constant value), and at every point, the limit is equal to the function (constant) value at that point.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuous Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 24th 2010, 11:03 PM
  2. Continuous functions help
    Posted in the Calculus Forum
    Replies: 8
    Last Post: March 5th 2010, 10:09 PM
  3. Continuous Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 23rd 2010, 06:06 AM
  4. continuous Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 18th 2009, 07:05 AM
  5. continuous functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 14th 2007, 09:57 AM

Search Tags


/mathhelpforum @mathhelpforum