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Math Help - Finding the values of k???

  1. #1
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    Finding the values of k???

    Let f be a piecewise defined function given by
    f(x) ={ k(k + 1) sin² (x) + 2e^kx cos(x), x < (π÷2),
    { x² + k (x - k + 1), x ≥ (π÷2)

    for some k Є R. Find the values of k for which f is continuous when x = (π÷2).


    please solve this including showing the workings.
    The 2 individual { brackets are supposed to be 1 large bracket but there is no large bracket sign i can use,so i used 2 { instead indicating just 1 {.
    Hope u understand what im saying.
    Try to show the workings and give a clear answer so i dont get confused with the whole thing.
    ÷ Є ∞ ○ π { ≤ ² ≥ ∩
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by federer View Post
    Let f be a piecewise defined function given by
    f(x) ={ k(k + 1) sin² (x) + 2e^kx cos(x), x < (π÷2),
    { x² + k (x - k + 1), x ≥ (π÷2)

    for some k Є R. Find the values of k for which f is continuous when x = (π÷2).


    please solve this including showing the workings.
    The 2 individual { brackets are supposed to be 1 large bracket but there is no large bracket sign i can use,so i used 2 { instead indicating just 1 {.
    Hope u understand what im saying.
    Try to show the workings and give a clear answer so i dont get confused with the whole thing.
    ÷ Є ∞ ○ π { ≤ ² ≥ ∩
    Since both parts of the function are continuous on the relevant regions to
    make the function continuous you need only that they are equal at n/2.

    So you need to solve:

    k(k + 1) (sin(n/2))^2 + 2e^(kn/2) cos(n/2)=n^2/4 + k (n/2 - k + 1)

    for k.

    RonL
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