Where is the master When x approaches 0, f (x) divided by x equals 0, Let f (x) be the infinitesimal of order p of X. is p > 1? Why? I feel that the result seems to be unable to determine the relationship between P and 1

Where is the master When x approaches 0, f (x) divided by x equals 0, Let f (x) be the infinitesimal of order p of X. is p > 1? Why? I feel that the result seems to be unable to determine the relationship between P and 1

p> Because f (x) also tends to zero, which is clearly stated in the book equivalent infinitesimal

Infinitesimal comparison of higher numbers
When two infinitesimals of numerator and denominator are compared, when can the numerator or denominator be substituted into the value of X?
At this point, the numerator and denominator are still zero. For example, if x tends to 0, LIM (SiN x * e ^ x) / x, can we substitute x = 0 into e ^ x first

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If infinitesimal multiplied by bounded function is 0, how much is infinitesimal multiplied by unbounded function?

Infinitesimals and unbounded functions are of order
For example, let X be infinitesimal
X * (1 / x) = 1. That is to say, the product of the first order infinitesimal and the first order unbounded function is a bounded number
In other words, x ^ 2 * (1 / x) = x tends to zero, that is, the answer of infinitesimal of higher order multiplied by unbounded function of lower order is 0
Similarly, the answer of higher order unbounded function multiplied by lower order infinitesimal is infinity

Is infinite times bounded function equal to 1?
I know that infinitesimal times bounded quantity tends to 0, so what is infinite (infinite sign) multiplied by bounded quantity? For example, when Lim x tends to infinity (sign), is x * sin (1 / x) equal to 1 fixed?
Which of the following limits is equal to 1? A. Lim x > infinite SiNx / X b.lim x > infinite x * sin (1 / x) C.Lim x > 0 x * sin (1 / x) d.lim x > 1 SiNx / X. at first, I chose C, but when the teacher analyzed the paper in class, he said it was B, so I was confused

It's all wrong upstairs!
Infinite multiplicative bounded function can not determine the result,
May be infinite;
Maybe it doesn't exist
When X - > 0,
The limit of (1 / x) * sin (1 / x) does not exist
1 / X - > tends to infinity, but sin (1 / x) is bounded!
It's not getting bigger and bigger, infinitely bigger
It's periodically getting bigger and bigger. There are infinitely many zeros in the middle! Where is infinity?
No matter how large x becomes, although sin (1 / x) tends to be zero and infinitesimal, there is still a function with solutions
Isn't infinitesimal bounded? It's more bounded and smaller
When x is infinite, (1 / x) * sin (1 / x) -- > 0
This is what your teacher should say
Or (1 / x) / sin (1 / x) -- > 1

Why is 1 / [b (B + β)] a bounded function? β is an infinitesimal
Don't you understand?

B (B + β)] is not equal to 0. Remove the two equal to 0

What is the multiplication of infinitesimals

The result is infinitesimal
I don't know the specific value. The limit value should be close to 0
From the exponential function image when the base is less than 1, when the index approaches infinity and the base approaches 0, the y-axis infinitely approaches 0

Is infinitesimal multiplied by bounded variable equal to 0?

Yes, obviously!

The product of infinitesimal and bounded variable is still infinitesimal. What is bounded variable? By the way, give an example to prove this theorem

sinx

Is it true that the product of infinitesimal and bounded quantity is infinitesimal?

Correct, I use this conclusion to solve many problems

The difference of bounded variables of limit infinitesimal
RT who can give detailed analysis

Infinitesimal is zero,
A bounded variable is in a region
For example, when the value of SiNx is positive, it is in [- 1,1]