Find the value of the constant c that makes the following function continuous on

Question

Find the value of the constant c that makes the following function continuous on (-infty,infty). f(b) = egin{cases}displaystyle{cb+1}& ext{if} bin left(-infty ,9 ight]cr displaystyle{cb^{2}-1}& ext{if} bin left(9,infty ight)end{cases} Find the value of the constant c that makes the following function continuous on (-infty,infty). f(b) = egin{cases}displaystyle{cb+1}& ext{if} bin left(-infty ,9 ight]cr displaystyle{cb^{2}-1}& ext{if} bin left(9,infty ight)end{cases} Find the value of the constant c that makes the following function continuous on (-infty,infty). f(b) = egin{cases}displaystyle{cb+1}& ext{if} bin left(-infty ,9 ight]cr displaystyle{cb^{2}-1}& ext{if} bin left(9,infty ight)end{cases}

Explanation / Answer

function will be continious on (-,) if it is continous at 9

limx->9+ f(b)

limx->9+ (cb2-1)

=c*92-1

=81c -1

f(9)=c(9)+1

=9c+1

f(b) is continous at b =9 ,if limx->9+ f(b) =f(9)

81c -1=9c+1

72c=2

c=2/72

c=1/36

c =1/36 makes f(b) continous at b =9

c =1/36 makes f(b) continous in(-,)

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