calc

posted by .

Consider the function f(x)=

x^2+a if x<0,
2x+a^2 if 0 less than or equal to x less than or equal to 1,
3 if x>1

a. determine the value(s) of a that will make f(x) continuous at x=0

b. determine the value or values of a that will make f(x) continuous at x=1

  • calc -

    I will be happy to critique your thinking.

  • calc -

    For part a I took the limit as x tends to zero from the right of 2x+a^2. I put zero in for x and then said a=0 which would also make the limit as x approaches zero from the left of x^2+a 0 so the function would be continuous.

    I don't know how to start part b because there is no variable for x>1

  • calc -

    You are correct, part of 3 is missing.

  • calc -

    Maybe the limit of x approaches 1 from the right of 3 = 3. And then set the limit of x approaches 1 from the left of 2x+a^2 = 3 and then solve for a and get 1.

  • calc -

    I am not certain I would make that assumption on the problem. However, you could be right.

  • calc -

    one more question.

    if possible determine the value(s) of a that will make f(x) continuous on (negative infinity, infinity)

  • calc -

    There is more than one value of a that will make the function continuous at x=0, since at x=0,
    x^2+a =2x+a^2
    or setting x=0,
    a-a²=0
    a(1-a)=0
    giving
    a=0 or a=1.

    Now you can continue with the last part.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math/Calculus

    Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that. could you please …
  2. calc again!

    i got answers for this one, but i feel like i did something wrong. f(x)= 2x+1 when x is less than or equal to 2 (1/2)x^2 + k when x is greater than 2 1) what value of k will make f continuous at x = 2?
  3. i lied. very quick calc problem.

    f(x) = abs(sin(x)), -pi less than or equal to x less than or equal to pi g(x) = x^2 let H(x) = g(f(x)) i got that H(x) would equal sin^2(x). THIS IS WHERE I AM STUCK! find the domain of H. do i still need to account for "-pi less than …
  4. stats

    Continuous Random Variable, I Let X be a random number between 0 and 1 produced by the idealized uniform random number generator described. Find the following probabilities: a.P(0less than or equal to X less than or equal to 0.4) b.P(0.4 …
  5. ap stats

    Continuous Random Variable, I Let X be a random number between 0 and 1 produced by the idealized uniform random number generator described. Find the following probabilities: a.P(0less than or equal to X less than or equal to 0.4) b.P(0.4 …
  6. Calculus

    A 0.2 ml dose of a drug is injected into a patient steadily for 0.75 seconds. At the end of this time, the quantity, Q, of the drug in the body starts to decay exponentially at a continuous rate of 0.2 percent per second. Using formulas, …
  7. Calculus

    Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than or equal to x, and x is less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
  8. calculus

    Consider the function f(x)=65x−cos(x)+2 on the interval 0 less than or equal to x less than or equal to 1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k?
  9. Algebra 2

    Okay so I need help with basically how to find the domain, range, and how to solve if it says Find the value of f(3). Let the f function be defined by f(x) = the square root of x + 1 for -1 is less than or equal to x less than or equal …
  10. Calculus

    Find the constants a and b such that the function is continuous on the entire line f(x){7, x is less than or equal to -3 ax+b, -3 is less than x is greater than 4 -7, x is less than or equal to 4

More Similar Questions