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Sequences and limits 
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#1
Jan3110, 04:16 PM

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1. The problem statement, all variables and given/known data
[tex] x_{n}(t) \left\{\begin{array}{cc}nt,&\mbox{ if } 0\leq t \leq \frac{1}{n}\\ \frac{1}{nt} & \mbox{ if } \frac{1}{n}\leq t \leq 1 \end{array}\right. [/tex] 2. Relevant equations 3. The attempt at a solution Can someone help me get started finding the limit as n > inf? I've never taken the limit of a sequence that has such a dependence on t. For t in [0, (1/n)], the values of the sequence will range between 0 and 1, and for t in [(1/n),1], the values will range between 0 and 1 as well. It doesn't really matter how large you take n... 


#2
Jan3110, 04:29 PM

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Pick a fixed x0 in [0,1] and think about limit x_n(x0) as n>infinity. If x0 is not zero there is always an N>0 such that 1/N<x0. That means for all n>N the definition of x_n(x0) is 1/(n*x0). What's the limit at x0?



#4
Feb110, 01:49 PM

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Sequences and limits



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