Lesson 1 Talk about your hobby

What you do in your free time:

  • get up to sth 做某事
  • like to do 是一种习惯, 都表明i enjoy it

  • like = fond of; passionate about; into doing sth

  • dabble in. means less seriously

  • an aficionado. not professional, not too seriously. i do sth for fun OR i do sth, but i am an amateur

How often you do it

  • whenever i can
  • as often as i can
  • whenever i get a chance
  • i don’t get round to doing sth as much as i would like

Different tenses

  • to take up painting; i am new to it. means start a hobby
  • decided to have a go at doing someth; decided to try my hand at doing sth. means to try sth new
  • i have been doing for as long as i can remeber; for donkey’s year. means do sth so long

i often paint. i decided to have a go at painting because my daughter was taking classes yeah, so, i’ve been painting for about 2 years.

The benefits of hobbies

  • to relax; to stay healthy, to socialise
  • it just help me __( unwind, kick back, chill out )
  • i find that it help me __( get int shape, keep fit, stay in shape )
  • it allows me to just __( to hang out with friend, to chill out with friends, to meet up with friends)
  • it’s quite a nice way to __ ()
  • it has a calming effect / therapeutic / stress buster;

2024/10/06 VIO简介

相机定位和IMU定位的优缺点:

方案 IMU 相机
优势 快速响应
不受成像质量影响
角速度估计准确
无漂移
直接测量旋转和位置
劣势 存在零偏
低精度会发散(大于几秒)
容易遮挡
移动快速时易丢失
旋转表现不好

Lesson 1

由于HEXO上配置LaTex过于麻烦,故将PDF直接插入到博客中。

2021/1/2 高数笔记

数列的极限:

设 $\vert x_{n}\vert$ 为一数列,如果存在常数 $a$ ,对于任意给定的数 $\varepsilon$ (不论他多么小),总存在正整数 $N$ ,使得当 $n>N$ 时,不等式 $\vert x_{n}-a\vert <\varepsilon$ 都成立,那么就称常数 $a$ 为数列 $\vert x_{n}\vert$ 的极限,或者称 数列 $\vert x_{n}\vert$ 收敛于 $a$ 记为

数列极限定理

1、收敛数列的有界性

如果数列 $\vert x_{n}\vert$ 收敛,那么数列 $\vert x_{n}\vert$ 一定有界
自我理解:由于数列不像函数,是离散的,所以数列的极限都是在N趋近于 $\infty$ 的时候取得的。还需要注意一点,数列有界是数列收敛的必要条件。
条件 $\rightarrow$ 结论,是充分性
结论 $\rightarrow$ 条件,是必要性

小tips:

$\underbrace{0.999\cdots9}_{n}-1=\frac{1}{10^{n}}$
分子上有根式时,可以将其化简到分母上
对于证明极限的题目,对不等式 $\vert x_{n}-a\vert <\varepsilon$ 进行适当放缩。



函数的极限

设函数 $f(x)$ 在 $x_{0}$ 的某一去心邻域内有定义,如果存在常数 $A$ ,对于任意给定的正数 $\varepsilon$ (不论其多么小),总存在正数 $\delta$ 使得当 $x$满足不等式 $0<\vert x-x_{0} \vert <\delta$ 时,对应的函数值 $f(x)$ 都满足不等式

那么常数A就称为函数 $f(x)$ 当 $x \rightarrow x_{0}$ 时的极限。

自我理解:如果一个函数存在极限,那么对于一个任意小的正数 $\varepsilon$,总能在 $x_{0}$ 的去心邻域内找到一个 $\delta$ ,使得该函数的上确界和下确界的差小于之前给定的 $\varepsilon$。也就是说 $\varepsilon$ 的取值是不受约束的。


对于该定理来说,很重要的一点是去心邻域,这表明即使函数在 $x_{0}$ 这个点没有意义,还是存在着极限值。

Lesson 1 A puma at large

单词:

  • puma n. 美洲狮
  • spot v. 看出,证据
  • evidence n.证据
  • accumulate v.累积
  • oblige v.使…感到必须
  • hunt v.追猎,寻找
  • blackberry n.黑莓
  • human being 人类
  • corner v.走投无路
  • trail n.一串
  • print n.印痕
  • cling v.粘
  • convince v.使…信服
  • somehow adv.不知道什么原因
  • disturb v.令人不安

词组:

  • be at large 潜逃
  • feel obliged to do 必须做某事
  • hunt for the remains of the .. 搜寻..的遗体

    Pick

  • pick cotton 采摘
  • pick and choose 挑选

    Proved

  • The search proved difficult 作为不及物动词时,表证明是
  • They proved her innocean 作为及物动词时,表证明

    Cling

  • cling to 粘/固守
  • His wet shirt cling to his body 粘在
  • She clings to the belief that her hubsband will come back 固守

    Complain

  • complain about the weather 抱怨…
  • complain of a headache 诉说…

    Disturb

  • sorry to disturb you 打扰
  • His strange behavious disturbed me 担心

A Few Tips

英文中表示一个事实的客观性使用被动语态

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