Why is Lim n times √ a = 0 when n tends to infinity

Why is Lim n times √ a = 0 when n tends to infinity

First of all, there is no value of A
If a = 0, then it is obviously zero
If a > 0, the limit is 1

The problem of Higher Mathematics in the sixth edition of Tongji is about the tendency of n to infinity
It's the fourth question of p65 exercise 1 - 8. I can't get the title. I hope students and teachers with textbooks can help me
My question is, when n tends to infinity, shouldn't we consider both positive infinity and negative infinity at the same time? If we consider both positive infinity and negative infinity, the result will be very different from that in the tutorial book
When Lim tends to infinity, do we need to consider whether it is positive infinity or negative infinity

The answer is correct. We don't need to consider the case of positive infinity and negative infinity here, because n here represents the N in the similar sequence, so n is a positive integer. Therefore, it can only approach to positive infinity. Generally, n is expressed as a positive integer, unless there is a special explanation. For example, if we tell you that n here approaches to negative infinity, then you have to consider the case of approaching to negative infinity, I hope my answer will be helpful to you. If x approaches infinity here, you should consider two situations: approaching positive infinity and approaching negative infinity. This is actually a small problem, but not paying attention to it will affect a lot of things

According to the definition, it is proved that f (x) = 5 / (x + 4) is infinite when x tends to - 4

Certification:
Take δ = 5 / m for any M
When 0