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Find the variable to make the function continuous

  1. Sep 4, 2012 #1
    Find k so that the following function is continuous on any interval.

    j(x) = {k cos(x), x ≤ 0
    {10ex − k, 0 < x

    2. Relevant equations

    3. The attempt at a solution
    I originally thought i had to check if the limits of both parts of the functions existed, and if so to set them equal to each other, but then I reread the question and realized that it wasn't asking me if its continuous, but to make it continuous by finding the value of k. I figured that i might be able to to set the two functions equal to each other to see if I can get k, but I'm not sure if that's right or not.
  2. jcsd
  3. Sep 4, 2012 #2

    Ray Vickson

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    For x > 0 do you mean 10*e*x - k, or do you mean 10*ex - k?

  4. Sep 4, 2012 #3


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    Maybe to give a 100% answer, just state that right of zero and left of zero there are

    no problems of continuity. Then , also, f is continuous if the value at a point coincides

    with the right- and left- limits.
  5. Sep 4, 2012 #4
    I'm sorry i meant 10*ex - k
  6. Sep 4, 2012 #5


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    Chose k to make the following two limits equal to each other.

    [itex]\lim_{x\to0^+}\,j(x)\,,[/itex] this is where j(x) = 10ex − k .

    [itex]\lim_{x\to0^-}\,j(x)\,,[/itex] this is where j(x) = k cos(x) .

    Then make sure that those limits equal j(0) (which of course, they will).
  7. Sep 5, 2012 #6
    I see. That helps. That's what i intended to to at first, but im not sure how i misinterpreted the question. Anyway thanks for all your help guys

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