## sequences and limits

1. The problem statement, all variables and given/known data

$$x_{n}(t) \left\{\begin{array}{cc}nt,&\mbox{ if } 0\leq t \leq \frac{1}{n}\\ \frac{1}{nt} & \mbox{ if } \frac{1}{n}\leq t \leq 1 \end{array}\right.$$

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...
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity
 Recognitions: Homework Help Science Advisor 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/NN the definition of x_n(x0) is 1/(n*x0). What's the limit at x0?
 What do you mean by pick and x0? You mean, pick a t0?

Recognitions:
Homework Help