Results 1 to 4 of 4

Math Help - Jump discontinuity, where?

  1. #1
    Raj
    Raj is offline
    Junior Member
    Joined
    Sep 2007
    Posts
    60

    Jump discontinuity, where?

    Code:
    Given this piecewise function
    f(x)=
    -x+b if x<-2
    5 if x=-2
    ((-5)/(x-b))+4 if x>-2
    
    For what value(s) of 
    
    
    
    
    b does 
    
    
    
    
    f have a (finite) jump discontinuity at −2? Write your answer in interval notation.
    I've been able to find the removable and infinite discontinuity and where it is continuous, but i've no idea how to find the interval where there is a jump.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    The answer is all values of b except -2,3


    since if lim f(x) is from the left exists
    2+ b = 5 b= 3



    Similarly if -5/(-2-b) + 4 = 5 then b = 3 makes the limit from the right
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Raj
    Raj is offline
    Junior Member
    Joined
    Sep 2007
    Posts
    60
    I don't think i understand, wouldn't that be infinite
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    If b = -2 then the right hand limit at -2 is infinite

    If b =3 we have removed the discontinuity at -2

    For any other value of b we have different right hand and left hand limits
    (but both are finite) hence we have a jump discontinuity
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. jump discontinuity proof for PDE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 2nd 2011, 10:00 AM
  2. IVT and Jump discontinuity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 11th 2011, 05:45 PM
  3. [SOLVED] Derivative with finite jump discontinuity?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2010, 08:16 PM
  4. How did he jump from this to that
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 28th 2010, 01:29 PM
  5. Replies: 2
    Last Post: November 27th 2008, 05:44 PM

Search Tags


/mathhelpforum @mathhelpforum