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Sheihuimin, Yun, Yi-Huai, Chanding-bian compilation of mathematical Analysis exercises Lecture notes section 16.2 exercises reference answers [from Tao younger brother]

Label:1. Set the known $ \sum\limits_{n = 1}^\infty {{{\left ({-1} \right)}^{n-1}}{a_n}} = A,\sum\limits_{n = 1}^\infty {{a_{2n-1 }}} = B $, proof: $ \sum\limits_{n = 1}^\infty {{A_n}} $ converge and ask for and.Solution: There is

Textbook fourth-indefinite integral exercise arrangement

Label:Trigonometric Correlation Types1. Using triangular changes and trigonometric identities, such as $\sin^2 x + \cos^2 x=1$ and twice-fold formula, and differential product, accumulation and difference.For example: 4-1 of 1-(5), so that $1=\sin^2

Application of Poj 4227 inverse tangent function

Label:Description 反正切函数可展开成无穷级数,有如下公式 (其中0 <= x <= 1) 公式(1) 使用反正切函数计算PI是一种常用的方法。例如,最简单的计算PI的方法: PI=4arctan(1)=4(1-1/3+1/5-1/7+1/9-1/11+...) 公式(2) 然而,这种方法的效率很低,但我们可以根据角度和的正切函数公式: tan(a+b)=[tan(a)+tan(b)]/[1-tan(a)*tan(b)]

Assignment 23 indefinite integral of several kinds of special functions

Label:(1)\[\begin{aligned}\int \frac{x}{x^2+2x-3}dx= \int \frac{x-1+1}{(x+3) (x-1)}DX= \int \frac{1}{x+3} + \frac14 \frac{4}{(x+3) (x-1)} DX\\=\int \frac{1}{x+3} + \frac14 \frac{(x+3)-(X-1)} {(x+3) (x-1)} DX= \int \frac{3/4}{x+3}-+ \frac{1/4}{x-1}

Cordic approximation algorithm

Tags: style blog http io color ar os using SPStart Learning Cordic algorithm nowLearn the blog:(1) trigonometric calculation, Cordic algorithm Introduction(1) A good explanation of the idea of

"Writing a program in C + + to find the value of pi"

Label:1 //Write a C + + program to find the value of pi2 /*3 Pi=16arctan (1/5) -4arctan (1/239)4 where arctan is calculated using the following form of pole number:5 arctan=x-(X^3/3) + (X^5/7)-(X^7/7) + ...6 */7#include <iostream>8 using

Assignment 22 Partial integration method for indefinite integral

Label:1.(1) Twice corner re-division integral(2)\[\int (\arcsin x) ^2 dx = (\arcsin x) ^2 x-2\int \frac{x}{\sqrt{1-x^2}} \arcsin x dx\]and\[\int \frac{x}{\sqrt{1-x^2}} \arcsin x dx=-\int \arctan x D (\sqrt{1-x^2}) =-\arcsin x \sqrt{1-x^2}-+\int dx=-\

Assignment 29 Generalized integrals

Label:1. (1)\[\mbox{original}= \lim_{b\to +\infty} \int_1^b \frac{e^2}{e^{2x}+e^2}dx= \frac1e \lim_{b\ to+\infty} \arctan (e^x/e) \bigg|_{1} ^B=\FRAC1E (\lim_{b\to +\infty}\arctan \frac{e^b}{e}-\frac{\pi}{4}) =\frac{\pi}{4

Mooculus calculus-2: Sequence and progression study Note 4. Alternating series

Tags: style http io ar color OS sp for strongThis course (MOOCULUS-2 "sequences and Series") was taught by Ohio State University on the Coursera platform in 2014.PDF textbook Download sequences and SeriesThis series of learning notes PDF download

Four-axis aircraft design Report

Tags: line of thought linear presentation comparative thesis design of frequency circuit of battery UniversityA report on the application of SCM in practical training design(Four-axis aircraft)Department: Department of Electrical Information

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