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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (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|The Limit of a Function

We hope it is apparent from the discussion in the last two frames that as we diminish the interval for $x$ around $x=3$, the values for $y=x^2$ cluster more and more closely about $y=9$. In fact, it appears that we can make the values for $y$ cluster as closely as we please about $y=9$ by merely limiting $x$ to a sufficiently small interval about $x=3$. Because this is true, we say that the limit of $x^2$, as $x$ approaches 3 , is 9 . We write this as
$$\lim {x \rightarrow 3} x^2=9 \text {. }$$ Let’s put this in more general terms. If a function $f(x)$ is defined for values of $x$ about some fixed number $a$, and if, as $x$ is confined to smaller and smaller intervals about $a$, the values of $f(x)$ cluster more and more closely about some specific number $L$, the number $L$ is called the limit of $f(x)$ as $x$ approaches $a$. The statement that “the limit of $f(x)$ as $x$ approaches $a$ is $L “$ is customarily abbreviated by $$\lim {x \rightarrow a} f(x)=L .$$
In the example at the top of the page $f(x)=x^2, a=3$, and $L=9$.
The important idea in the definition is that the intervals we use lie on either side of the point of interest $a$, but that the point itself is not included. The value of the function $f(a)$ when $x=a$ may be different from $\lim _{x \rightarrow a} f(x)$, as we shall see.

To summarize the mathematical argument in more familiar language: in the spirit of “Anything you can do I can do better!” the challenge to an opponent is “Pick a point as close as you want to $L$ as you please, and I can find a point close to a for which $f(x)$ will be closer to $L$ than the point that you chose.”

## 数学代写|微积分代写Calculus代写|Velocity

Our discussion has become a little abstract, so before we go on to differential calculus, let’s talk about something down to earth: motion. As a matter of fact, Leibniz and Newton invented calculus because they were concerned with problems of motion, so it is a good place to start. Besides, you already know quite a bit about motion.

Go to 117.
117
In this chapter, we will only consider motion along a straight line. Here is a warm-up problem.

A train travels away at a velocity $v \mathrm{mph}$ (miles per hour). At $t=0$, it is distance $S(0)=S_0$ from us. (The subscript on $S_0$ is to avoid confusion. $S_0$ is a particular distance and is a constant; $S(t)$ is a function that gives the distance the train is from us at time $t$.) Write the equation for $S(t)$ in terms of time $t$. (Take the unit of $t$ to be hours.)
$$S(t)=$$
Go to 118 for the answer.
118
If you wrote $S(t)=S_0+v t$, you are correct. Go on to frame 119 .
If your answer was not equivalent to the above, try to convince yourself that this answer is correct. Note that it yields $S_0$ when $t=0$, as required. The equation is that of a straight line, and it might be worthwhile reviewing the section on linear functions, frames 23-39, before continuing. Whenever you are satisfied with this result,

Here is a plot of the positions at different times of a train going in a straight line. Obviously, this represents a linear equation. Write the equation for the position of this train (in miles) in terms of time (in hours).
$$S(t)=$$
Find the velocity of the train from your equation.
$$v=$$

# 微积分代考

## 数学代写|微积分代写微积分代写|函数的极限

$$\lim {x \rightarrow 3} x^2=9 \text {. }$$让我们把它写得更一般化。如果定义一个函数$f(x)$为$x$的值关于一个固定的数字$a$，并且如果$x$被限制在关于$a$的越来越小的区间内，而$f(x)$的值越来越靠近某个特定的数字$L$，当$x$接近$a$时，这个数字$L$被称为$f(x)$的极限。“当$x$接近$a$时，$f(x)$的极限是$L “$”这句话通常被缩写为$$\lim {x \rightarrow a} f(x)=L .$$

## 数学代写|微积分代写calculus代写|Velocity

.

$$S(t)=$$

118

$$S(t)=$$

$$v=$$

## 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。

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