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On the problem of de centring neighborhood in Higher Mathematics When learning advanced mathematics, I encounter a problem: The neighborhood can be represented by {x | a - R < x < x + R} Then, if point a is removed, it becomes a de centered neighborhood, which can be expressed as: {x | 0 < | X - a | < R} I just can't turn around now. Why can I see | X - a | < R at a glance? Although I know that | X - a | < R is definitely right, I can't see it at a glance and ask for advice
The neighborhood can be represented by {x | a - R < x < A + R}. You wrote it wrong
Here we can see that a on both sides of the inequality changes from x-a. you can't move slowly at a glance
Then - R
De centered neighborhood problem This is what I see in the de centring neighborhood. U (a, δ) Why do I see in advanced mathematics today that u (a) has no back δ, What does this mean and what is its significance?
The U (a) norm refers to the de centered neighborhood of a, but there is No δ Scope of
Does lobida's law necessarily require differentiability in the domain of a point If the function is second-order differentiable at x = 0, can we use lobida's law to find the second-order derivative? Or can we only use definitions?
Of course, it is necessary to satisfy the differentiability in the definition domain of the function you want to use lobida's law. You can refer to the university textbooks for this problem. I hope you can understand it as soon as possible
Why does lobida's law require "de centring neighborhood differentiability"
Because lobida's law itself is the problem of finding derivatives. It must be differentiable in the field of centring to find the upper and lower derivatives of molecular denominators at the same time. Centring is to find the limit. Lobida's law is to find the limit when x tends to a certain number. Therefore, this number is the so-called heart. If you don't go to the heart, the so-called limit will be meaningless. In high school
What is lobida's law? How to find the limit, a simple example,
Example: LIM (x - > + infinity) (x ^ 2-1) / (2x ^ 2 + 2x + 1)
=LIM (x - > + infinity) (2x) / (4x + 2)
=LIM (x - > + infinity) 2 / 4
=1/2
About lobida's law The example in the book Lim x → + ∞ LNX / x ^ n (n > 0) I know how to do it. The use condition of lobida is that both up and down tend to 0. Ln X and x ^ n don't seem to tend to 0
Up and down all tend to infinity. You can use lobida's law
In principle, amorphous problems can be solved by lobida, but only by ln or e transformation
RELATED INFORMATIONS
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