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Homework Help: Continuity problem

  1. Sep 25, 2004 #1
    Hi, I have just one more problem :) here it is:

    (because I don't know how to do theta, "@" will equal theta)

    Find a value of K so that f(2) is continuous at @=0

    ( != means "not equal")

    Code (Text):
    f(@) = ( (2sin@)/@ , @ !=0 )
           ( 5k , @=0 )
    f(@) is a piecewise function

    I don't know how to get started on this problem, any help would be much appreciated :)
     
  2. jcsd
  3. Sep 25, 2004 #2
    The simplest way would be to set 5k = lim(@->0)[2sin(@)/@]

    Using l'hopital's rule, lim(@->0)[2sin(@)/@] = lim(@->0)[2cos(@)/1]

    I think you can do the rest :)
     
    Last edited by a moderator: Sep 25, 2004
  4. Sep 26, 2004 #3
    Whops, it shoudl be f(@) not f(2)

    So,

    5k = (2sin(@))/@

    k = [(2sin(@))/@]/5

    Would that work, or did I totally miss your point?
     
  5. Sep 26, 2004 #4
    I think you may have because that doesn't work. that function is not defined at @ = 0 so you have to use limits. k = 1/5 * limit[@->0](2sin(@)/@)
     
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