F (x) = x / (x + 1), when x0 = 2, find its nth order Taylor formula

F (x) = x / (x + 1), when x0 = 2, find its nth order Taylor formula

Classmate, this problem is actually very simple
Simplify f (x) = x / (x + 1) to 1-1 / (x + 1)
The second term is 1 / (x + 1), which can be transformed into 1 / (X-2 + 3), and the coefficient is 1 / 3
It can be changed to 1 / 3 * 1 / [1 + (X-2) / 3]
U = (X-2) / 3 can be replaced by substitution method, which can be changed to 1 / 3 * 1 / (1 + U)
The expansion of 1 / (1 + U) is very simple, which is 1 + (- U) + (- U) ^ 2 + (- U) ^ 3 +. + (- U) ^ n
Replace u with (x - 2) / 3, and the problem will be solved
Give me 30 points

What is the nth order Taylor formula with peyano type remainder of F (x) = LNX expanded by the power of (X-2)
F (x) = LNX is expanded by the power of (X-2) and calculated by ln (X-2)?

F (x) = LNX develops into Taylor's formula (Peano remainder) at x0 = 2. By using ln (1 + x) = x - X & # 178 / 2 + X & # 179 / 3 +. + (- 1) ^ (n-1) x ^ n / N + O (x ^ n) f (x) = LNX = ln [2 + (X-2)] = LN2 + ln [1 + (X-2) / 2] = LN2 + (X-2) / 2 - (X-2)

Taylor formula Title: F (x) = LNX by (X-2) power expansion with payano remainder n Taylor formula!
1. In the process of finding, f ∧ (n) (x) = (- 1) ∧ n-1 (n-1)! / X ∧ n this is the n-order derivative of F! Is the n-order derivative calculated or how?
2. How does f Λ (n) (2) = - 1 Λ n-1 (n-1)! / 2 Λ n get the result of (- 1) Λn-1 / N * 1 / 2 Λ n (X-2) Λn in the penultimate step of Taylor formula (the step before o [(X-2) Λn])

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Do not understand the contact again

5 * 6 * 9 * 8 * 13 * 10 * 17 * 12 *? * 25

21 14

It is known that the complex number satisfies (1) Z + 5 / Z ∈ (1,4]
(2) The real part and imaginary part of Z are integers, so we can find the complex Z

Using the principle of the important role of geographical environment in social development, this paper explains the importance of building a resource-saving society

The capacity and self purification capacity of geographical environment are limited. When the ecological damage and environmental pollution of human beings exceed their limits, it will lead to the increase of natural disasters and bring disaster to human beings. Therefore, we must adhere to the strategy of sustainable development, develop ecological agriculture, clean production, take the road of circular economy and build a resource-saving society!

Is it or are when there are plural nouns and singular nouns
Your trousers( )dirty,you must have ( )washed.
A.is,it B.are,it C.are ,them D.is,them
How to choose is or are for this kind of question

C
Trousers itself is a word in the plural. The predicate verb after trousers should be in the plural

Cut a cube into the largest cylinder. The surface area of the cylinder is 471 square centimeter

The height of the largest cylinder is equal to the edge length of the square, and the diameter of the bottom is equal to the edge length
Let the edge length of a square be a,
Surface area of cylinder = 2 bottom areas + side areas = 2 * 3.14 * A / 2 * A / 2 + 3.14 * a * a
= 3.14 * 3 / 2 * a * a = 471 square centimeter
So a * a = 100, a = 10 cm
So the volume of the cylinder is 3.14 * 10 / 2 * 10 / 2 * 10 = 785 cubic centimeters

The least common multiple of two integers is 1925. These two integers are divided by their greatest common divisor, and the sum of the two quotients is 16. These two integers are______ And______ ．

1925 = 5 × 5 × 7 × 11, 11 + 5 = 16; so the two quotients should be 11 and 5; 5 × 7 × 5 = 175, 5 × 7 × 11 = 385; answer: these two integers are 175 and 385 respectively; so the answer is: 175385

In the triangle ABC, ab = AC, the center line BD on AC divides the perimeter of the triangle into two parts: 21 cm and 9 cm, and calculates the length of each side of the triangle?
How many

Let the waist length be x cm and the base be y cm,
There are two cases
x+x/2=21,
x/2+y=9
x=14,y=2
x+x/2=9,
x/2+y=21,
x=6,y=18
6+6