Posted by **Mishaka** on Saturday, October 22, 2011 at 8:32pm.

If the following function is continuous, what is the value of a + b?

f(x) = {3x^2 - 2x +1, if x < 0

a cos(x) + b, if 0 </= x </= pi/3

4sin^2(x), if x > pi/3

A. 0

B. 1

C. 2

D. 3

E. 4

I know that since the function is continuous, it should be equal to 1 at 0 and 3 at pi/3 (To follow the other two pieces of the function). From here, I am having a great deal of difficulty figuring out what coordinates would make the function work in this way. Any help is appreciated.

- Calculus (Continuity) -
**MathMate**, Saturday, October 22, 2011 at 11:02pm
At x=0, a*cos(0)+b = 1 = 3x^2-2x+1

=> a+b= 1 = 3(0)-2(0)+1

At x=π/3,

a*cos(π/3) + b = 1 = 4sin^2(π/3)

=> (a/2) + b = 3/2 = 2*3/4

But you don't need to solve for a and b if only a+b is required. (see second line).

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