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Math Help - Converge 61.13

  1. #1
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    Converge 61.13

    Prove: If lim xn = L as (n approaches infinity) the lim abs(xn) = L. (Hint: The inequality abs(abs(a) - abs(b)) is less than equal to abs(a-b).

    abs= absolute value
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  2. #2
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    well, they gave you the solution.

    we have |x_n-L|<\epsilon, and ||x_n|-|L||\le|x_n-L| so we're done.
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  3. #3
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    Quote Originally Posted by tigergirl View Post
    Prove: If lim xn = L as (n approaches infinity) the lim abs(xn) = L. (Hint: The inequality abs(abs(a) - abs(b)) is less than equal to abs(a-b).

    abs= absolute value
    Are you told that L\ge 0? If not, you can't prove it, it isn't true! What is true in general is that is [math\lim x_n= L[/tex] then \lim |x_n|= |L|.
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