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Math Help - How To Show Work For This Limit, And Solve For K?

  1. #1
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    How To Show Work For This Limit, And Solve For K?

    1. lim (5/(2-x))
    x->2^+
    (coming from the right)'
    My work:
    5/(2-2) = 5/0
    lim (5/(2-x)) = -infinite because...?
    x->2^+

    I know it equals negative infinite, but don't know how to show the work. I did a graph in my head...

    2. What values of k is the function f(x) continuous on (-infinite, infinite)?
    f(x) =
    x+k^2, x<2
    kx^2 + 14, x=>2

    My work:
    x + k^2 = ck^2 + 14
    x + k^2 - ck^2 - 14 = 0.

    Can somebody clear up these questions?
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  2. #2
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
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    Florida
    Posts
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    1. because 2 - x < 0 for x > 2


    2. f(x) =
    x+k^2, x<2
    kx^2 + 14, x=>2


    you want lim f(x) as x approaches 2- and 2+ to be the same:

    2+k^2 = 4k + 14

    k^2 -4k -12 = 0

    (k-6)(k+2) = 0 k = 6 or -2

    x + k^2 = ck^2 + 14
    x + k^2 - ck^2 - 14 = 0.
    Where did the c come from ?
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