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Math Help - find constants a and b so function is continuous

  1. #1
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    find constants a and b so function is continuous

    I am having trouble with this problem :

    Find constants a and b so that the function is continuous for all x ∈, where

    f(x)={sin(ax)/bx, x<0
    2, x=0
    ax+b, x>0
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  2. #2
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    Quote Originally Posted by sydewayzlocc View Post
    I am having trouble with this problem :

    Find constants a and b so that the function is continuous for all x ∈, where

    f(x)={sin(ax)/bx, x<0
    2, x=0
    ax+b, x>0
    f(x) is continuous for x\neq0

    f(x) is continuous at x = 0 if \lim_{x\to 0}f(x)=f(0)

    We want \lim_{x\to 0^-}\frac{sin(ax)}{bx}=2 and \lim_{x\to 0^+}ax+b=2

    \lim_{x\to 0^-}\frac{sin(ax)}{bx}=\lim_{x\to 0^-}\frac{a cos(ax)}{b}=\frac{a}{b}

    \frac{a}{b}=2 so a=2b

    \lim_{x\to 0^+}ax+b=b

    b=2 and a=4
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