# Thread: I'm trying to find the values of a and b that are continuous within this function!

1. ## I'm trying to find the values of a and b that are continuous within this function!

I was able to find be but I'm having trouble with a. b is 81/cos(18pi)

2. ## Re: I'm trying to find the values of a and b that are continuous within this function

$f(2^-) = a \sin(2\pi)+ b = b$

$f(2^+) = 2^2 + a = 4+a$

For continuity at $x=2$ we must have $b = a+4$

$f(9^-) = 9^2 + a = 81+a$

$f(9^+) = b \cos(2\pi 9)+a = (a+4)\cos(18\pi)+a = 2a+4$

Similarly for continuity at $x=9$ we must have

$81+a = 2a+4$

$a=77$
$b = 81$