Say the limit of infinitesimal is 0, right?

Say the limit of infinitesimal is 0, right?

A variable whose limit is the number of zeros. Specifically, when the independent variable x is infinitely close to x0 (or the absolute value of x increases infinitely), the function value f (x) is infinitely close to zero, that is, f (x) = 0 (or F (x) = 0), then f (x) is called the infinitesimal when x → x0 (or X →∞). For example, f (x) = (x-1) 2 is the infinitesimal when x → 1, f (n) = is the infinitesimal when n →∞, f (x) = SiNx is the infinitesimal quantity when x → 0. In particular, it should be pointed out that a small number should not be confused with an infinitesimal quantity
Beginners should note that the infinitesimal is the limit of the function rather than the quantity 0, which means that the limit of the independent variable is the quantity 0 under a certain change mode. If a function is an infinitesimal, we must explain the change trend of the independent variable. For example, X ＾ 2-4 is the infinitesimal when x → 2, but we can't generally say that x ＾ 2-4 is an infinitesimal
Infinitesimal quantities are usually represented by lowercase Greek letters, such as α、β、ε Wait, sometimes α (x)、 ο (x) And so on, indicating that the infinitesimal is a function of X
Infinitesimal quantities have the following properties:
1. The algebraic sum of finite infinitesimal quantities is still infinitesimal
2. The product of finite infinitesimal quantities is still infinitesimal
3. The product of a bounded function and an infinitesimal is an infinitesimal
With the concept of infinitesimal, we will naturally associate it with the concept of infinity. What is infinity?
Definition of Infinity: when the independent variable x tends to a, the absolute value of the function increases infinitely, then f (x) is called infinity when x → A. It is recorded as Lim, f (x) = ∽, X → a
Similarly, infinity is not a specific number, but an infinite development trend. No matter how large a constant is, it is less than +

Use the properties of infinitesimal to calculate the following limits (1) Limx ^ 2cos1 / x where x tends to 0 (2) Lim [(arctanx) / x] where x tends to infinity

1. Cos1 / X is a bounded function, so the boundedness of infinitesimal multiplication is still infinitesimal
limx^2cos1/x=0
2. Arctanx is equivalent to X
So Lim [(arctanx) / x] = LIM (x / x) = 1

The relationship between limit and infinitesimal " Theorem: if limf (x) = a, then f (x) = a + A, where Lima = 0; Conversely, if f (x) = a + A and Lima = 0, then limf (x) = a Can you explain the derivation process of this theorem, or give an example? I don't understand it I just don't understand one thing: limf (x) = a, then f (x) = a + A, where Lima = 0; This f (x) = a + A, how can a function f (x) be equal to the constant a + A as the limit

Infinitesimal is close to 0, but not equal to 0. If limf (x) = a, then f (x) = a + A, where Lima = 0, f (x) = a + a holds only when Lima = 0. On the contrary, if f (x) = a + A and Lima = 0, then limf (x) = a, since Lima = 0, limf (x) = a is not equal to constant a + A, it is an infinite approach, just like. When n tends to

As for the relationship between function limit and infinitesimal, if the value of a function is equal to its limit plus infinitesimal, can it be said that the value of a function is equal to its limit minus infinitesimal?

LIM (x - > x0) f (x) = a, let u (x) = f (x) - A,
Then f (x) = a + U (x), and lim (x - > x0) U (x) = 0,
That is, the value of the function is equal to its limit value plus infinitesimal@
Let V (x) = a - f (x),
Then f (x) = a - V (x), and lim (x - > x0) V (x) = 0,
That is, the value of the function is equal to its limit minus infinitesimal
@It's a common saying

If the function tends to be infinitesimal (i.e. 0), does the function have a limit

Yes, the limit is 0
There is a limit for the sequence of equal differences with a tolerance of 0,
If the common ratio Q satisfies 0 < | Q | < 1 or q = 1, there is a limit,
The first n terms and Sn of the equal difference sequence with the first term of 0 and the tolerance of 0 have limits,
The common ratio Q satisfies the existence of the limit of the first n term and Sn of the equal ratio sequence of 0 < | Q | < 1

What is the difference between the product of 2.8 and 1.4 minus the quotient of 7.8 divided by 6?

two point six two