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Math Help - Calculus I Homework Help

  1. #1
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    Exclamation Calculus I Homework Help

    Let f(x) = 2 Domain: x less than or equal to -1
    = ax+b Domain: -1 less than x or less than 3
    = -2 Domain: x greater or equal to 3

    Find a and b such that f is continuous.
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  2. #2
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    Quote Originally Posted by Nimmy
    Let f(x) = 2 Domain: x less than or equal to -1
    = ax+b Domain: -1 less than x or less than 3
    = -2 Domain: x greater or equal to 3

    Find a and b such that f is continuous.
    Hello, Nimmy,

    I've attached a diagram to show you what you have to calculate:

    In short: There are 2 points which are connected by a straight line. So you know 2 points of this line. Use the 2-point-formula of a line to get the equation.

    (You should get f(x)=-x+1, -1 < x < 3)

    Greetings

    EB
    Attached Thumbnails Attached Thumbnails Calculus I Homework Help-ger_stckweis.gif  
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  3. #3
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    Quote Originally Posted by Nimmy
    Let f(x) = 2 Domain: x less than or equal to -1
    = ax+b Domain: -1 less than x or less than 3
    = -2 Domain: x greater or equal to 3

    Find a and b such that f is continuous.
    It x\not = -1, x\not= 3 it is certainly countinous because there are constant and linear function where are always countinous.
    However we need to check x=-1,3
    Let us do -1 first,
    By definition of countinuity we need that,
    \lim_{x\to -1} f(x)=f(-1)
    Thus,
    \lim_{x\to -1^-}f(x)=\lim_{x\to -1^+}f(x)=2
    But the limit from the left is same as,
    \lim_{x\to -1^-}2=2
    And the limit from the right is same as,
    \lim_{x\to -1^+}ax+b=-a+b
    Thus,
    -a+b=2
    Similarly, if we do this for x=3 we have,
    3a+b=-2
    From these two equations we have,
    a=-1,b=1
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