Results 1 to 11 of 11

Math Help - continuity of a function on intervals

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    3

    continuity of a function on intervals

    hi guys
    2nd year uni student here...havent taken math 30 pure for 3 years so i am regretting theh calculus i am doing, even though it may seem easy to many of you:
    2x + x^2/3 on [-1,1]

    ...can someone walk me through a question like this and explain it in simpleton terms thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by roguetrader View Post
    hi guys
    2nd year uni student here...havent taken math 30 pure for 3 years so i am regretting theh calculus i am doing, even though it may seem easy to many of you:
    2x + x^2/3 on [-1,1]

    ...can someone walk me through a question like this and explain it in simpleton terms thanks
    What?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    3
    Quote Originally Posted by VonNemo19 View Post
    What?
    is the function continuous on the given interval
    2x + x^(2/3) on [-1,1]
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by roguetrader View Post
    is the function continuous on the given interval
    2x + x^(2/3) on [-1,1]
    The function 2x+\sqrt[3]{{x^2 }} is continuous on every interval.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jan 2010
    Posts
    3
    Quote Originally Posted by Plato View Post
    The function 2x+\sqrt[3]{{x^2 }} is continuous on every interval.
    why? can someone run me through how to get that solution?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    A well defined function on its domain is continuous there.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by roguetrader View Post
    why? can someone run me through how to get that solution?
    The answer to that question is: probably not.
    Unless you can tell us what makes a function discontinuous.
    Can you tell us that? If not I doubt you will follow any explication.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by roguetrader View Post
    why? can someone run me through how to get that solution?
    Check for differentiability.

    Also, have a look at the definition of continuity.

    We say A function f(x) is continuos on an interval [a,b] if

    f(x) is defined on [a,b]

    \lim_{x\to{c}}f(x)=f(c) for all c\in(a,b)

    and

    \lim_{x\to{c}}f(x) Exists for all c\in(a,b)
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,792
    Thanks
    1687
    Awards
    1
    Quote Originally Posted by Krizalid View Post
    A well defined function on its domain is continuous there.
    Surely that depends upon what one means by ‘well defined’.
    I certainly consider  f(x) = \left\{ {\begin{array}{rl}<br />
   {x - 1,} & {x < 1}  \\<br />
   {x^2 ,} & {x \geqslant 1}  \\ \end{array} } \right. well defined on [-1,1].
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,971
    Thanks
    1638
    Quote Originally Posted by Krizalid View Post
    A well defined function on its domain is continuous there.
    Ouch! I would say that "f(x)= 1 if x\le 0, -1 if x> 0" is "well defined" but certainly not continuous on its domain!

    It is true that our ways of writing functions have developed so that any function we are able to write as a single formula is continuous wherever it is defined but that an artifact of the way we write formulas and has nothing to do with being "well defined".
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    ahhh, i think that's not what i meant to say, i mean if \text{Dom}f=\mathbb R then f is continuous on \mathbb R.

    that's what i said about "well defined."
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Continuity of Function on Intervals
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 2nd 2010, 08:50 PM
  2. Intervals of Continuity
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 30th 2009, 01:45 PM
  3. find intervals with just one root of function
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: May 30th 2009, 10:42 PM
  4. Intervals where the function is Increasing
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 18th 2009, 06:43 PM
  5. continuity intervals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 24th 2007, 07:13 PM

Search Tags


/mathhelpforum @mathhelpforum