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Math Help - Showing limits

  1. #1
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    Showing limits

    can anyone helpme out with this? gahh...soo hard!

    i have to show that lim (1/(x^2 + 1) )= 1 as x --> 0

    using limit's definition!
    and now i did

    |f(x) - L | = | 1/(x^2 + 1) - 1|
    | x - 0 | < delta

    what does one do from here? im soo stuck


    thanks!!
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  2. #2
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    Quote Originally Posted by matlabnoob View Post
    i have to show that lim (1/(x^2 + 1) )= 1 as x --> 0
    using limit's definition!
    Try 1 > \varepsilon  > 0\quad  \Rightarrow \quad \delta  < \sqrt {\frac{\varepsilon }{{1 - \varepsilon }}}
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  3. #3
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    thank you!

    but how does that show the limit tends to 1? ........ im confused with it
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  4. #4
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    Quote Originally Posted by matlabnoob View Post
    thank you!

    but how does that show the limit tends to 1? ........ im confused with it
    You must show that if \left| {x - 0} \right| < \delta then \left| {1 - \frac{1}{{1 + x^2 }}} \right| < \varepsilon .

    Now if you expect to have it done for you then you out of luck with me.
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  5. #5
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    Quote Originally Posted by Plato View Post
    You must show that if \left| {x - 0} \right| < \delta then \left| {1 - \frac{1}{{1 + x^2 }}} \right| < \varepsilon .

    Now if you expect to have it done for you then you out of luck with me.
    i knew this.thanks anyway
    ill attempt again
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