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Earn +20 ptsQ: What sequence has no upper bound but does not tend to infinity?
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What is a cauchy sequence?
(xn) is Cauchy when abs(xn-xm) tends to 0 as m,n tend to infinity.
Every uniformly convergent sequence of bounded function is uniformly bounded?
The answer is yes is and only if da limit of the sequence is a bounded function.The suficiency derives directly from the definition of the uniform convergence. The necesity follows from making n tend to infinity in |fn(x)|
What does tends to infinity mean?
When we say as a variable n tends to infinity, we mean as n gets very very large. For example. If we look at 1/n as n tend to infinity, then n gets very large and 1/n goes to zero.
What are the asymptotes of a logarithmic function?
As x tends towards 0 (from >0), log(x) tend to - infinity. As x tends to + infinity so does log (x), though at a much slower rate.
The time period of a simple pendulum having infinite length will be?
It would tend towards infinity
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