Results 1 to 6 of 6

Math Help - Value of the constant c: continutity question

  1. #1
    Member mybrohshi5's Avatar
    Joined
    Sep 2009
    Posts
    230

    Value of the constant c: continutity question

    For what value of the constant is the function continuous on where





    f(y)= (y^2) - c if y E (-inf,5)
    cy + 5 if y E [5,inf)




    i have no idea where to even start on this. for some reason i think its going to be a simple one. maybe not.


    could i get some help please.


    thank you


    chad
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Aug 2009
    From
    Gothenburg, Sweden
    Posts
    37
    Look att the function when y=5. What do have to hold for f(y) to be continous when y=5?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by mybrohshi5 View Post
    For what value of the constant is the function continuous on where





    f(y)= (y^2) - c if y E (-inf,5)
    cy + 5 if y E [5,inf)




    i have no idea where to even start on this. for some reason i think its going to be a simple one. maybe not.


    could i get some help please.


    thank you


    chad
    Since this function is piecewise, and we know that it is continuous everywhere except possibly at y=5, we must analyze this point.

    To ensure continuity at y=5, All we must do is make

    \lim_{y\to5^-}f(y)=\lim_{y\to5^+}f(y)

    So, we write

    \lim_{y\to5^-}(y^2-c)=\lim_{y\to5^+}(cy+5)

    Can you finish?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member mybrohshi5's Avatar
    Joined
    Sep 2009
    Posts
    230
    No i guess i cant finish it. i understand why you set the limits equal to each other but i guess i cant figure out how to get an exact value for c?

    thank you for the help
    Follow Math Help Forum on Facebook and Google+

  5. #5
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by mybrohshi5 View Post
    No i guess i cant finish it. i understand why you set the limits equal to each other but i guess i cant figure out how to get an exact value for c?

    thank you for the help
    It's easy my friend! Solve for c!

    implies that y^2-c=cy+5



    So, all you gotta do is solve the system.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member mybrohshi5's Avatar
    Joined
    Sep 2009
    Posts
    230
    thank you. i tried that earlier after you posted the first time but could not solve for c.
    i got it now though. im not having a great math morning lol

    thank you again
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: September 18th 2010, 07:42 PM
  2. continutity
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 1st 2010, 09:17 PM
  3. constant function question
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: November 4th 2009, 12:47 PM
  4. Question involving arbitrary constant
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: July 10th 2009, 12:28 PM
  5. Replies: 5
    Last Post: February 29th 2008, 02:05 PM

Search Tags


/mathhelpforum @mathhelpforum