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Finding value of c that makes function continuous

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  1. Sep 26, 2016 #1
    1. The problem statement, all variables and given/known data
    f(x)= (sincx/x) ; x<0
    1+(c)(tan2x/x) ; x≥0

    2. Relevant equations


    3. The attempt at a solution
    Lim as x tends to 0+
    = 1+c⋅2⋅(sin2x/2x)⋅(1/cos2x) =1+c⋅2⋅1⋅1= 1+2c

    Lim as x tends to 0 - = (sincx/x)=(c/1)⋅(sinx/x)=c⋅1=c

    Equating both: 1+2c=c
    c=-1

    ∴For the function to be continous at x=0, c=-1

    Is my answer correct?
     
  2. jcsd
  3. Sep 26, 2016 #2

    Mark44

    Staff: Mentor

    Looks good to me.
     
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