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Math Help - Continuity problems help?

  1. #1
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    Continuity problems help?

    Hi friends

    how i solve it!

    find the value of ( a ) so that given function f(x) is continous.

    when f(x) is x^2+a if -2 < x < 2

    6at if x=2

    x-2 if x>2

    please help me
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  2. #2
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    Quote Originally Posted by mathbee View Post
    Hi friends

    how i solve it!

    find the value of ( a ) so that given function f(x) is continous.

    when f(x) is x^2+a if -2 < x < 2

    6at if x=2

    x-2 if x>2

    please help me
    I assume that you mean:

    f(x)=\left\{\begin{array}{rcl}x^2+a&~if~&-2<x<2 \\ 6at&~if~& x=2  \\ x-2&~if~&x>2\end{array}\right.

    1. Since \lim_{x\to 2^+}f(x) = 0 you can determine a because \lim_{x\to2^-}f(x) must be zero too.

    2. Now calculate t such that f(2)= \lim_{x\to2^-}f(x) = \lim_{x\to 2^+}f(x)
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