If the limit of X tends to positive infinity and negative infinity is different (that is, X tends to infinity), it can only show that when X tends to positive infinity, the limit is A and X tends to infinity, and their limits exist separately. If A=B, it can be directly said that the limit of X tending to infinity exists, that is, A or B, but if A and B are different, the limit of X tending to infinity does not exist. You can refer to Exercise 2 on page 38 and Example 2 on page 35 of Advanced Mathematics 5th Edition and Example 1 and below on page 57 of Higher Education Press.