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Math Help - Well behaved functions

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    Well behaved functions

    which of the following are not well behaved funtions:
    a)ax^2 + bx+c
    b)e^x for all x
    c)y= |x|
    d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
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    Quote Originally Posted by myoplex11 View Post
    which of the following are not well behaved funtions:
    a)ax^2 + bx+c
    b)e^x for all x
    c)y= |x|
    d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
    "Well-behaved" is a term mathematicians use because they are lazy to state all the conditions a function must meet. Hence this term is not well-defined. You need to say what it means over here.
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    Quote Originally Posted by myoplex11 View Post
    which of the following are not well behaved funtions:
    a)ax^2 + bx+c
    b)e^x for all x
    c)y= |x|
    d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
    (sigh)
    Would you eat \pi? No. So don't spell it "pie," spell it correctly: "pi."

    Okay, this might be what you need: y = |x| is not "smooth." That is to say all the derivatives of y are not continuous. (In fact no derivative of this function is continuous.) In this sense y = |x| is not well behaved.

    -Dan
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  4. #4
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    Quote Originally Posted by myoplex11 View Post
    which of the following are not well behaved funtions:
    a)ax^2 + bx+c
    b)e^x for all x
    c)y= |x|
    d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
    Quote Originally Posted by topsquark View Post
    (sigh)
    Would you eat \pi? No. So don't spell it "pie," spell it correctly: "pi."

    Okay, this might be what you need: y = |x| is not "smooth." That is to say all the derivatives of y are not continuous. (In fact no derivative of this function is continuous.) In this sense y = |x| is not well behaved.

    -Dan
    d) is not even continuous at +/- pi

    RonL
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