### 数学代写|微积分代写Calculus代写|Algebra Review

statistics-lab™ 为您的留学生涯保驾护航 在代写微积分Calculus方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写微积分Calculus代写方面经验极为丰富，各种代写微积分Calculus相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|微积分代写Calculus代写|Real number line

The first numbers a child learns are the counting numbers, $1,2,3, \ldots$, and so on, also known as the natural numbers N. These numbers are pictured on a horizontal line, equally spaced, with larger numbers to the right and smaller numbers to the left (figure 1).

Next one learns the integers Z, which include the natural numbers, their negatives, and zero. These are also placed on the number line (figure 2).

Then came numbers of the form $\frac{a}{b}$, where $a$ and $b$ are integers. These are the rational numbers $\mathbf{Q}$. Rational numbers are also placed proportionally on the number line, as always with larger numbers to the right and smaller numbers to the left. It is common to represent numbers as points on a line, as shown in figure 3 . Rational numbers have decimal expansions that either terminate or repeat, such as
$$\frac{1}{2}=0.5$$
or
$$\frac{4}{3}=1 . \overline{3}=1.33333 \ldots$$
Irrational numbers have decimal expansions that neither terminate nor repeat, such as $\sqrt{2}=1.4142 \ldots$ and $\pi=3.14159 \ldots$. They also find their place on the number line. The collection of all of these numbers is called the real numbers $\mathbf{R}$ (figure 4). The real numbers fill out the number line; they can be placed in one-to-one correspondence with the points on the line. Even so, stay tuned for more numbers in chapter 1!

## 数学代写|微积分代写Calculus代写|Inequalities

The statement $ab$ means the number $a$ is greater than the number $b$, and $a$ is to the right of $b$ on the number line. Notice in figure 5 that although 1 is to the left of 3 on the number line, $-1$ is to the right of $-3$. Thus, $1<3$, but $-1>-3$. When multiplying (or dividing) an inequality by a negative number, the direction of the inequality must be reversed.The same is true when taking reciprocals. Although $2<7$, notice in figure 6 that $\frac{1}{2}>\frac{1}{7}$. The larger the denominator, the smaller the fraction.

Solving linear inequalities is similar to solving linear equations. Care must be taken, however, to change the direction of the inequality under the circumstances just described.
Example 1 Solve the inequality $4 x+2<x-7$.
Solution First we subtract $x$ from both sides:
$$3 x+2<-7$$
Next we subtract 2 from both sides:
$$3 x<-9 .$$
Finally, we divide both sides by 3 :
$$x<-3 .$$
The solution to the inequality is $x<-3$.
Solutions to inequalities may also be presented in graphical form. The idea is to indicate which numbers on the number line satisfy the inequality. For $x<-3$, the variable $x$ satisfies the inequality as long as $x$ is to the left of $-3$ (figure 7 ):

Figure 7 The inequality $x<-3$, shaded in green. The open circle indicates that $-3$ is not included

Drawing an open circle indicates the point is not included. An alternate version that is sometimes used is to draw a parenthesis instead (figure 8 ).
Recall that $a \leq b$ means that either $a<b$ or $a=b$.
Example 2 Solve the inequality $-7 x+1 \leq 4$.

## 数学代写|微积分代写Calculus代写|Intervals

Interval notation, and the various types of intervals, are summarized in table 1. Parentheses indicate the endpoint is not included; brackets indicate the endpoint is included. The symbols $\infty$ and $-\infty$ are not numbers, but merely indicators that the interval has no endpoint on the right or the left, respectively. Intervals that do not contain any of their endpoints are open intervals; intervals that contain all of their endpoints are closed intervals. Because neither $\infty$ nor $-\infty$ are endpoints, then $[a, \infty)$ is a closed interval. Bounded intervals have two endpoints; unbounded intervals range to $\infty$ or $-\infty$. The two numbers or symbols in the interval are always written with the smaller value or $-\infty$ on the left and the larger value or $\infty$ on the right. In table 1 , the green shading on the graphs indicates the solution set.

Solution (a) Because 3 is not included, we use a parenthesis for that endpoint, and because 5 is included, we use a bracket for that endpoint. The interval is $(3,5]$.
(b) The interval is neither open nor closed because it contains one, but not the other, endpoint. The interval is bounded because it does not range to $\infty$ or to $-\infty$.
Example 4 Graph the interval: $(a)[4, \infty),(b)(-5,-3)$.
Solution (a) The interval $[4, \infty)$ includes 4 , so we draw a filled circle at 4 to indicate its inclusion. The shading (green) has no bound on the right.
(b) For the interval $(-5,-3)$ we do not include either endpoint, so we draw open circles at $-5$ and at $-3$. The shading (green) is between those two numbers.

Intervals are characterized by the property that all numbers between two of the interval’s numbers are also in the interval. If there is any “gap” in the set, then it is not an interval. The set $(-4,0) \cup(3,5)$ is not an interval; see figure 11 .

12=0.5

43=1.3¯=1.33333…

3X+2<−7

3X<−9.

X<−3.

## 数学代写|微积分代写Calculus代写|Intervals

(b) 区间既不开也不闭，因为它包含一个端点，但不包含另一个端点。区间是有界的，因为它的范围不为∞或者−∞.

(b) 对于区间(−5,−3)我们不包括任何一个端点，所以我们在−5并且在−3. 阴影（绿色）位于这两个数字之间。

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。