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Math Help - Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

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    Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

    Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

    I'm having a hard time visualizing it.
    Last edited by mr fantastic; October 2nd 2011 at 08:21 PM. Reason: Copied title into main body of post.
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    Re: Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

    Quote Originally Posted by gummy_ratz View Post
    I'm having a hard time visualizing it.
    Maybe because \displaystyle x is only defined for \displaystyle x \in [0, 1]... How can you possibly make \displaystyle x\to\infty when the function does not even exist there?
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    Re: Why does cos[n(x+1)] for n->00 fail to have a limit at every x on [0,1]?

    The function doesnt exist as n->00? I'm looking for a function cont. on fn:[0,1]->[0,1] that fails to have a limit for every x in [0,1], and when integrating it from 0 to 1 as n->00 it equals 0. I thought I read somewhere that this fit the description?
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