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Here is a time sample: $Q = \{(t_i, x_i) | 0 \leq x_i \leq x_{i+1}, 1 \leq i \leq n\}$

and rules:

(1) $T_1 \leq t_{i+1} - t_i < T_2$ where $T_1, T_2 > 0$

(2) $x_i$ comes with error:

$x_i = \lfloor x(t_i) \rfloor$ where $\lfloor x \rfloor$ - whole part of $x$, $x(t_i)$ - voluntary unknown law of object motion.

How we can find (approximately but sufficiently accurate) speed of the object at the given time?

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    I must be dumb, I don't understand this question. :/2010-08-11
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    I have tried to convert to latex. If I messed up please let me know/edit it.2010-08-24
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    I think $x_{t_i}$ should be changed back to $x(t_i)$. There are two x's in this problem. The subscripted $x_1,\dots,x_n$ are a given list of numbers, while $x(t)$ is a function.2010-08-24
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    @Laurent: Fixed that. Please let me know if there is more to be fixed.2010-08-24
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    Yes, the subscripted $x_1,…,x_n$ are a given list of numbers obtained by the measurement system, while $x(t)$ is a unknown nondecreasing function that describes the path traveled by the object at the given time (it's similar to the total number of steps traversed in a trip).2010-11-21

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