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Why is an unbounded variable not necessarily an infinite variable, and an infinite variable must be an unbounded variable When f (x) = xsinx, xn (n subscript) = pi / 2 + 2npi, f (x) tends to infinity When x m (M subscript) = m * PI, f (x) is equal to 1 Why is it said that it is an unbounded variable but not an infinite variable
Infinity is the infinite increase of | f (x) | in a certain change process of X
For f (x) = xsinx, when x tends to infinity, | f (x) | does not tend to infinity, because it always has a point of zero
So xsinx is unbounded, but not infinite
(when x m (M subscript) = m * PI, f (x) equals 0)
Unbounded sequence is not necessarily infinite. Who can give an example
Example:
The sequence of 1,0,2,0,..., N, 0,... Must be unbounded in the process of increasing N, but it is not infinite, because infinity requires that all the following terms should be greater than a large positive number m starting from a certain term, which is impossible for this sequence
I'm glad to answer for you. I hope it can help you,
"Unbounded sequence is not necessarily infinite sequence", right? Why?
If you mean that the limit is infinite, then this conclusion is correct
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