English translation Go forward side by side with 2. Lag behind 3 continuously 4. Interdisciplinary

English translation Go forward side by side with 2. Lag behind 3 continuously 4. Interdisciplinary

1 stay aware of or use stay up-to-date with
2 fall behind/back
Fall can be replaced by drop
3 successfully or in a row
4 interrelated subjects
Interdisciplinary, plural
English translation
1 in fact
Never
Not considered or studied
Changeable weather
1 as a matter of fact
2 by no means
3 on trust
4 uncertain weather / changeable weather
English translation
Stable life .I hope with you
I do not say you understand
Some things,some people,you don't care
You can be destined to that person
Peaceful life. I hope to be with you
I can't say you understand
Some things, some people, you don't care
But you are destined to be with that person
A stable life. I want to be with you.
I do not say you understand there is something wrong with the grammar. I didn't say that. Do you understand?
Some things, some people, you don't have to care too much.
You are destined to belong to that person.
A stable life. You and I hope I don't say you understand that some things, some people, you don't care, you can be doomed to this person
I hope to live a stable life with you
I don't say, you know
Some things, some people, I don't care
You may be destined to be like that
Stable life, I hope to be with you
I didn't say you would understand
Some things, some people, you don't care
You can be the one you're meant to be
I want to live a stable life with you
I don't say you understand
You don't care about things and people
But you are the one I was meant to be
Safe life, I hope to be with you. I won't say that you understand some people and things, but you don't care. For that person, you are the one who is meant to be.
Stable life. I hope with you. You and I hope
I do not say you understand.
Some things,some people,you don't care。 Some things, some people, you don't care
You can be destined to that person.
I hope I can live a peaceful life with you
I don't say it, you know it
Some things, some people, you don't have to care
He / she is the one you are meant to be
Put With Comparative English phrase translation
compare to
compare A with B
compare with
On the understanding of periodic functions,
There is a saying in the book
For a periodic function, if there is a minimum positive number in all the periods, it is called the minimum positive period
I have two questions about this sentence
Q1: why should we emphasize "for periodic functions"? Isn't there a period for periodic functions?
Q2: why do we say that if there is a minimum positive number? Is there any case that does not exist? Is the period negative or infinite in the case that does not exist?
1. Period is the concept of periodic function, but non periodic function does not
For example, for any positive function y = 2, it does not exist
In this formula, t cannot be negative! That's the definition
It is not a periodic function. There is no period
Which is the smallest positive number of the minimum positive period
For example, the minimum positive period is a
But the period can be any multiple of a, say - A - 2A or 2A
These are its periods, but they can't be infinite
If there is no existence, there is no period, it is not infinite
The problem of solving the range of logarithmic function
The function y = log2 (X & sup2;
+2) The value range of is______ I don't ask for ranges,
By the way, how to find the range of logarithmic function.
X ^ 2 + 2 > = 2, so log2 (X & sup2; + 2) > = log2 (2) = 1, so the range is [1, positive infinity]
For a function of the form y = loga (f (x)),
1 find the range U of F (x) first
2 find the intersection K of u and (0, positive infinity)
3K if the shape is like [b, positive infinity], look at a, A1, then the answer is [loga (k), positive infinity]
If K is like [b, C], look at a, A1, then the answer is [loga (b), loga (c)]
5 if u is the union of more than one case, then the union of one part and one part of the range can be obtained, and finally the union of the range can be obtained
x²≥0
So x & sup2; + 2 ≥ 2
So log2 (X & sup2; + 2) ≥ 1
So the range is [1, positive infinity]
Let u = x & sup2; + 2, then u ∈ [2, + ∞]
∴f（x）=log2（x²+2）∈【1，+∞】
Is the monotonicity of function and inverse function necessarily the same?
I mean, if these two functions are in different intervals, but they are both increasing or decreasing functions, can we say that they have the same monotonicity?
Isn't monotonicity for intervals? So the interval of function and inverse function is not the same, why do they have the same monotonicity?
You can't say that
It depends on whether they are monotone functions on the union of these two intervals
Proof of periodicity of Dirichlet function
The rational number is x (d) = 1
0 x is an irrational number
(1) If t is not an irrational period
If D (1) = 0, D (1 + T) = 1, it does not satisfy the definition of periodic function
(2) If t is any nonzero rational number
If x is an irrational number, x + T is also an irrational number, D (x) = 0 = D (x + T)
If x is a rational number, x + T is also a rational number, D (x) = 1 = D (x + T)
So D (x + T) = D (x)
So any nonzero rational number is a period
Why can a calculator work out log? Don't logarithmic functions have bases and true numbers
The log on the calculator is the common logarithm by default, which is actually LG
The base has been set to 10 by default
If there is no log8, it should be LG8. The base number is 10 and the true number is 8
Monotonicity of functions. Inverse functions
1. The increasing area of 5-4x-x ^ 2 under the function y = root?
2. The monotone decreasing interval of 2x ^ 2-3x-2 under the function y = root?
3. Monotone decreasing interval of function y = 5x + 1 / 3?
4. If f (x) is an increasing function in the interval (- 2.3), then y = the increasing interval of F (5 + x)?
5. Given that the inverse function of the function y = x + 2 of X + A is itself, then a =?
6. Given that the function y = f (x) has an inverse function, then in the same coordinate system, the image of y = f (x) in x = f ^ - 1 (y) is (how?) the image of y = f (x) and y = f ^ - 1 (x) is (how?)
7. If f (x) is a linear function and f [f (x)] = 4x-1, find the analytic expression of F (x)?
Hope to have the process of solving the problem
1.[-5,-2]
2. (negative infinity, - 1 / 2]
3. Whole range
4.(-7,-2)
5.a=-1
6. The same for y = x symmetry
7.a=2,b=-1/3; a=-2,b=1