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Math Help - make me continuous

  1. #1
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    make me continuous



    Find the values of a and b that make f continuous everywhere.

    I see a polynomial. should I factor it? I kinda want to factor it haha.

    anyway, I know I gotta focus on x=3. If I can get the two points to be continuous there, I should be good, right?
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by leftyguitarjoe View Post


    Find the values of a and b that make f continuous everywhere.

    I see a polynomial. should I factor it? I kinda want to factor it haha.

    anyway, I know I gotta focus on x=3. If I can get the two points to be continuous there, I should be good, right?
    There's no need to factor the polynomial (the second one ).

    You gotta focus on x=3 but also on x=1 !
    And yes, it should be good.

    Let f_1(x)=\frac{x^2-1}{x-1}=x+1, x<1
    Let f_2(x)=ax^2-bx+5, 1 \le x<3
    Let f_3(x)=2x-a+b, x \ge 3

    A function is continuous at x=a if :
    \lim_{\substack{x \to a \\ x<a}} f(x)=\lim_{\substack{x \to a \\ x>a}} f(x)
    So for example at x=1 :
    \lim_{\substack{x \to 1 \\ x<1}} f(x)=\lim_{x \to 1} f_1(x)

    and \lim_{\substack{x \to 1 \\ x>1}} f(x)=\lim_{x \to 1} f_2(x)


    Same for x=3, see what expression it is if x<3 and if x>3
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  3. #3
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    oh, I see now. The limits should be the same when approaching from the left and right?
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  4. #4
    Moo
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    Quote Originally Posted by leftyguitarjoe View Post
    oh, I see now. The limits should be the same when approaching from the left and right?
    Yes
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  5. #5
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    Quote Originally Posted by Moo View Post
    Yes
    cool! thanks!
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