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Math Help - Bonus Question involving Continuity?

  1. #1
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    Bonus Question involving Continuity?

    I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

    Thx in advance!
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    Quote Originally Posted by Solid8Snake View Post
    I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

    Thx in advance!
    Let f:I\mapsto I continually ([tex]I=[0,1]). Let g(x)=f(x)-x. More obvious now. Consider the function at the endpoints.
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    I am not quite sure what you mean by what you wrote. Can you please explain in more depth.

    thanks.
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    Quote Originally Posted by Solid8Snake View Post
    I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.

    Thx in advance!

    lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Solid8Snake View Post
    I am not quite sure what you mean by what you wrote. Can you please explain in more depth.

    thanks.
    Think about it this way, h(x)=f(x)-x h(0)=f(0)0\geqlsant 0-0=0[/tex] if it's zero we're done. Otherwise it's greater than zero. Similarly h(1)=f(1)-1\leqslant 1-1=0. If it's equal zero zero we're done. Otherwise it's less than zero.
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by vince View Post
    lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today
    What a stupid thing to say.
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    I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.
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    Quote Originally Posted by Solid8Snake View Post
    I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.
    What does the IVT say?
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    whether there is a root within a given interval
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Solid8Snake View Post
    whether there is a root within a given interval
    Not really. Look it up, look at what I said and get back to me.
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  11. #11
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    well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)
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    so in other words would this be sort of what we are getting at
    0<c<1?
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    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Solid8Snake View Post
    well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)
    Ok, so we know that h(0)\geqslant 0 and [math\h(1)\leqslant 0[/tex] if either are zero we're done, so assume that neither are. Then h(0)>0,h(1)<0
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  14. #14
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    I think I get it now.

    Thanks for the help!
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  15. #15
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    Quote Originally Posted by Drexel28 View Post
    What a stupid thing to say.
    easy for you to say




    ... most of the problems are fun for me, so in some sense i should thank them ...lol...cornfest.
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