Calculus (Continuity)

posted by .

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) -

    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).

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval?
  2. Calculus

    COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval?
  3. Calculus

    consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval?
  4. Calculus

    COnsider g(x)=(8)/(x-6) on (6,13) (a) Is this function continuous on the given interval?
  5. Calculus

    consider k(t)=(e^t)/(e^t-7) on[-7,7] Is this function continuous on the given interval?
  6. Calculus (Continuity)

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

    Is this the right explanation for this question 1. Examine the continuity of the function h(x)= -x, if x<0 0, if x=0 x, if x>0 Answer: Since h(x)= -x, if x<0 0, if x=0 x, if x>0 is h=|x|, we can conclude that the function …
  8. Calculus - #6

    If the following function is continuous, then what is the value of b?
  9. Continuity Calculus Help

    The given function is defined for all x > 0 except at x = 8. Find the value that should be assigned to f(8), if any, to guarantee that f will be continuous at 8. (If an answer does not exist, enter DNE.) f(x)= Sqrt( x^2-64/x-8)
  10. Continuity Calculus Help

    Find the value of constants c and d that make the function below continuous at x = 4. f(x) = x2 − 3x x < 4 c x = 4 d + x x > 4 c = d = 8 I got d=8, but finding c is giving me trouble.

More Similar Questions