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Math Help - Continuity: finding b

  1. #1
    Junior Member mant1s's Avatar
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    Continuity: finding b

    Hi Community,

    been trying to work out this continuity problem to find b. Could someone please take a look at my work?

    Code:
    Problem:
    if f(x) is a function that is continuous then we must have b = ?
    
    piecewise:
    
    f(x) = 8x - 4 , x <= 5
            -3x - b , x > 5
    My work...

    Code:
    5 = f(5-) = f(5+)
    5 = -3(5) + b
    20 != b
    Thank you!
    Last edited by mant1s; June 7th 2009 at 08:03 PM.
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  2. #2
    Behold, the power of SARDINES!
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    f(x)=\begin{cases}8x-4, \mbox{ if } x \le 5 \\ -3x-b, \mbox{ if } x > 5 \end{cases}

    \lim_{x \to 5^-}8x-4=36

    Now

    \lim_{x \to 5^+}-3x-b=-15-b

    Now to be continous the above must be equal so

    36=-15-b \iff b=-51

    so we get

    f(x)=\begin{cases}8x-4, \mbox{ if } x \le 5 \\ -3x+51, \mbox{ if } x > 5 \end{cases}
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by mant1s View Post
    Hi Community,

    been trying to work out this continuity problem to find b. Could someone please take a look at my work?

    Code:
    Problem:
    if f(x) is a function that is continuous then we must have b = ?
     
    piecewise:
     
    f(x) = 8x - 4 , x <= 5
            -3x - b , x > 5
    My work...

    Code:
    5 = f(5-) = f(5+)
    5 = -3(5) + b
    20 != b
    Thank you!
    For a funnction to be continous at x=c, we must have

    \lim_{x\to{c^-}}f(x)=\lim_{x\to{c^+}}f(x)

    Therfore

    \lim_{x\to{5^-}}(8x-4)=\lim_{x\to{5^+}}(-3x-b)

    \Longleftrightarrow{8(5)-4}=-3(5)-b

    You can do the rest
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  4. #4
    Junior Member mant1s's Avatar
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    Thanks guys for your help, but wouldn't the answer be 51 instead of -51?
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