1. 1, 1, 2, 1/2,...，n， 1/n ....
Infinity means that a subsequence is infinite, but it does not guarantee that the whole sequence is infinite.
2.an = 1/n，bn = n^2
{bn} can be taken arbitrarily, as long as an is not 0, anbn can be an arbitrary number.
3. When x is not equal to 0, define f(x) as f (x) = x 2; Define f(0) = 1.
If x0 = 0, a = LIMF (x) = LIM x 2 = 0 when x tends to 0.
If the function is continuous, LIMF (x) = f (x0) > 0, but for discontinuous functions. A has nothing to do with f(x0), and may not be greater than 0, but a >: = 0.