Calculation of anomalous integral ∫ 1 / X ∧ 3 DX (1, + ∞)

∫ （1,+∞） 1/x^3 dx
=-x^(-2)/2|（1,+∞）
=-1/2+limx^(-2)/2
=-1/2+0=-1/2

Calculation of anomalous integral: ∫ (1,2) [x / √ (x-1)] DX=
Where 1 is the lower limit and 2 is the upper limit,

Let √ (x-1) = t, then x = T ^ 2 + 1, x from 1 to 2, then t from 0 to 1
The original formula is equal to
∫(1,2) (t^2+1)/t d(t^2+1)
= ∫(0,1) 2(t^2+1) dt
= 8/3

The value of ∫ (upper limit positive infinity, lower limit 0) DX / (√ (x * (x + 1) ^ 5)) is () A. infinity b.0 C.2 / 3 D.1

No answer & nbsp; the answer is 4 / 3
Using MATLAB & nbsp; to get the result
syms x
int(1/sqrt(x*(x+1)^5),0,inf)
ans =4/3
In addition, the points of their own
Let x = Tan θ ^ 2
be

How to prove the limit of monotone bounded sequence

The explanation of this theorem in Tongji textbook is: for this theorem, we don't prove it, we just give its geometric meaning on the number axis. You can refer to it. If you want to test this problem, you won't test theorem proving, but you need to prove the monotonicity of a certain sequence first, and then prove the boundedness of the sequence, so as to get that the sequence must be convergent, In other words, there is a limit, and then take the limit assumption as a on both sides of the known equation satisfied by the sequence, and then solve the equation to get a, which is the limit value of the sequence. In short, it is to find two conditions according to this criterion, so as to explain the existence of the limit, and then calculate the limit value

The problem of example 1 on page 57 of Tongji University advanced mathematics fifth edition
For example 1, if you don't understand it, please tell me carefully why the second step of the equation is equal to the long one,

Factorization x ^ n-1 = (x-1) [x ^ (n-1) + x ^ (n-2) + Replace x with the radical

Why is the a option of the second and third problem in the general exercise of Tongji 6th edition of higher mathematics wrong

Because H - > + ∞, then 1 / h - > 0+
We can only say that f (x) has right limit at x = a
If f (x) is differentiable at x = a, it holds only when both left and right limits exist and are equal
So we have to consider the left limit
A option has only the right limit

Recommendation of advanced mathematics exercise book of Tongji Sixth Edition
Hello everyone! I'm a freshman this year. We are studying advanced mathematics of Tongji sixth edition, but I don't think there are any exercises in it. It's hard to consolidate my knowledge. Please recommend a good exercise book with detailed answers. Thank you

There are a lot of exercises at the end of every lesson in the book. Do you think it's too simple? You can go to the big Xinhua Bookstore and buy them (in Beijing, you can buy them on the fourth floor of Xidan Book Building). I think "advanced mathematics intensive speaking" (from Beijing Normal University) and "advanced mathematics problem solving guide" (from Beijing Normal University) are very good. They are all layered exercises. I'm also a beginner, But I think these two books are of great help to me. Now it's much easier than when I was just studying

The fifth major problem in Chapter 6-2 of Tongji Sixth Edition
Find the area of the figure enclosed by the following curves
（1）ρ=2a cosθ
Let's talk about the specific method
And how to find the angle range

Take a good look at the meaning of the two variables in polar coordinates and their relationship with rectangular coordinates in the book. Don't just remember the formula. If you are not used to polar coordinate equation, you can first change it into rectangular, so as to draw a sketch and judge the variation range of ρ and θ. ρ * ρ = 2A ρ cos θ, X & sup2; + Y & sup2; = 2aX, (x-a) & sup2; + Y & sup

Are the solutions of the exercises of Tongji 5th Edition and 6th edition the same
I have the complete solution book of the sixth edition of Tongji, but the book is higher mathematics of the fifth edition of Tongji

There are not many changes in the whole exercise, but there are still changes. Moreover, the content order of the book is also different. The 5th edition of analytic geometry and vector algebra is in the first volume, and the differential equation is in the second volume. The 6th edition of analytic geometry and vector algebra is in the second volume, and the differential equation is in the first volume

Calculation of anomalous integral ∫ 1 / X ∧ 3 DX (1, + ∞)