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Math Help - Definition of Continuous function.

  1. #1
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    Definition of Continuous function.

    Hi all member.
    Can any one help me to demonstrat that (by definition ):
    does the folowing function is continuous at x=2.
    f(x)=1/(1+x^4).
    Thanks.
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  2. #2
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    Re: Definition of Continuous function.

    Will be continuous if

    1. f(x) exists for x=2

    2. \displaystyle \lim_{x\to 2}f(x) must also exist

    3. f(2) = \displaystyle \lim_{x\to 2}f(x)
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  3. #3
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    Re: Definition of Continuous function.

    Quote Originally Posted by Lamalif View Post
    Hi all member.
    Can any one help me to demonstrat that (by definition ):
    does the folowing function is continuous at x=2.
    f(x)=1/(1+x^4).
    If you are looking for a \epsilon-\delta proof the you need
    \left| {\frac{1}{{1 + x^4 }} - \frac{1}{{17}}} \right| = \frac{{\left| {16 - x^4 } \right|}}{{17\left( {1 + x^4 } \right)}} \leqslant \left| {2 - x} \right|\left| {2 + x} \right|\left| {4 + x^2 } \right|

    You can control the size of |x-2| factor and bound the other two.
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