placed repetition
今日复习计划 2025年5月 周一 周二 周三 周四 周五 周六 周日 19 20 21 22 23 24 25 26 27 28 29 30 31 2025年6月 周一 周二 周三 周四 周五 周六 周日 1 2 3 4 5 6 7 8 ...
words-twelfth-day
单词释义 tuition - n. paraphrase: money paid for teaching synonym: fee, charge example: Although tuition is expensive, many students take loans because education is valuable for their future careers. tentative - adj. paraphrase: not certain or fixed synonym: uncertain, provisional example: We made tentative plans to meet on Saturday, but we might change them if the weather turns bad. inaugurate - v. paraphrase: to formally start something new synonym: launch, begin example:...
数一大纲
2025 年考研数学一大纲原文(完整版) 考研考试形式和试卷结构 一、试卷满分及考试时间 试卷满分为150 分,考试时间为180 分钟. 二、答题方式 答题方式为闭卷、笔试. 三、试卷内容结构 高等教学约 60%6 0 \%60% ;线性代数约 20%2 0 \%20% ;概率论与数理统计约 20%.2 0 \% .20%. 四、试卷题型结构: 单选题10 小题,每小题5 分,共50 分 填空题6 小题,每小题5 分,共30 分 解答题(包括证明题)7 小题,共70 分 高等数学 一、函数、极限、连续 函数的概念及表示法、函数的有界性、单调性、周期性和奇偶性、复合函数、反函数、分段函数和隐函数、基本初等函数的性质及其图形、初等函数、函数关系的建立; 数列极限与函数极限的定义及其性质、函数的左极限和右极限、无穷小量和无穷大量的概念及其关系、无穷小量的性质及无穷小量的比较、极限的四则运算、极限存在的两个准则;单调有界准则和夹逼准则、两个重要极限： limx→ 0sinxx=1 \operatorname* { l i m } _ { x \to 0 } { \frac {...
常数项级数的审敛法
和这一节对比着看 一、正项级数审敛法（所有项 an≥0a_n \geq 0an≥0） 正项级数的收敛性仅需判断其部分和是否有上界，以下是具体方法： 1. 基本定理 若部分和数列 {Sn}\{S_n\}{Sn} 有上界，则级数收敛；否则发散。 2. 比较判别法 直接比较法： 若存在自然数 NNN，使得当 n>Nn > Nn>N 时 0≤an≤bn0 \leq a_n \leq b_n0≤an≤bn，则： ∑bn\sum b_n∑bn 收敛 ⇒∑an\Rightarrow \sum a_n⇒∑an 收敛； ∑an\sum a_n∑an 发散 ⇒∑bn\Rightarrow \sum b_n⇒∑bn 发散。 典型应用：与几何级数（如 ∑rn\sum r^n∑rn）或 ppp-级数（如 ∑1np\sum \frac{1}{n^p}∑np1）比较。 一道例题 例题： 判断级数 ∑n=1∞1n2+n\sum_{n=1}^{\infty} \frac{1}{n^2 + n}∑n=1∞n2+n1 的敛散性。 解： 我们要判断级数...
三重积分与曲线曲面积分习题总结
好难总结啊,都是技巧性的东西 type one:解三重积分 截面法 例：设几何体 Ω\OmegaΩ 由 z=x2+y2z = \sqrt{x^2 + y^2}z=x2+y2 与 z=1z = 1z=1 围成, 则∭Ω(z+x2) dv=\iiint\limits_{\Omega} (z + x^2) \, dv =Ω∭(z+x2)dv= 截面法的特点就是被积函数光由z组成，看到光由z组成的项立马想到截面法 对称性、奇偶性 例：设 L:y=x2(0≤x≤1)L: y = x^2 (0 \leq x \leq 1)L:y=x2(0≤x≤1), 则 ∫Lx y ds=_____\int_L x \, y \, ds = \_\_\_\_\_∫Lxyds=_____. 例：设几何体 Ω=((x,y,z)∣x2+y2+z2≤R2,z≥0)\Omega = \left( (x, y, z) \mid x^2 + y^2 + z^2 \leq R^2, z \geq 0 \right)Ω=((x,y,z)∣x2+y2+z2≤R2,z≥0), 其中 Ω1\Omega_1Ω1 为...
Meet The New Amazon Robot That Can Feel What It Touches
video [Segment 1: Introduction to Amazon’s Vulcan Robot] Amazon’s new robot Vulcan doesn’t look like a person or move like one. This is the robotic gripper. This is the hand. These are paddles that can squeeze the item. But it’s doing a job that until now, only people at Amazon could do, stowing thousands of items into bins. Our hands are one of the most amazing parts of our bodies. And it’s that physical intelligence, that physical AI that we’re trying to give to the Vulcan robots. While...
向量代数与空间解析几何习题总结
type one：给一条直线求绕轴旋转的曲面方程 直线 L:x−12=y−2−1=z1L: \frac{x-1}{2} = \frac{y-2}{-1} = \frac{z}{1}L:2x−1=−1y−2=1z 绕 zzz 轴旋转而成的曲面为______. 这一道题有点迷啊 以下讨论是在M和M0M_{0}M0在z坐标相同的那一个圆中进行的 设M：（x，y，z）是曲面上的任意一点，M0：(x0,y0,z)M_{0}：(x_{0},y_{0},z)M0：(x0,y0,z)是直线上的一点 原点设为R:(0,0,z) 可以得到这个关系：∣MR∣=∣MM0∣|MR|=|MM_{0}|∣MR∣=∣MM0∣，然后把x0,y0x_{0},y_{0}x0,y0用z来代替就得出结果了 不过还是好奇怪，就是理不清思路 搁置吧 type two：求点到直线的距离（这个重要） 点 M(2,1,1)M(2, 1, 1)M(2,1,1) 到直线 L:x−11=y−10=z−1L: \frac{x-1}{1} = \frac{y-1}{0} =...
words-eleventh-day
单词释义 sentiment - n. paraphrase：a feeling or opinion synonym：feeling, thought, view example：Although the team lost the game, there was a positive sentiment among the players because they had played their best, which made the coach proud. reign - n./v. paraphrase：(n.) the period when a king or queen rules a country; (v.) to rule as king or queen synonym：rule, govern, period example：During her reign, the queen introduced many reforms, which improved the lives of her people, and she was...
word-tenth-day
单词释义 reverse - v./n./adj. paraphrase：to go backward or change to the opposite synonym：undo, invert example：If you accidentally delete a file, you can reverse the action by pressing Ctrl+Z, which is a handy feature unless you’ve already closed the program. refute - v. paraphrase：to prove something wrong synonym：deny, disprove example：Although the scientist presented strong evidence, her critics tried to refute her claims by pointing out minor flaws in the data. household...
words-ninth-day
单词释义 mature - adj./v. paraphrase：fully grown or developed synonym：grown, ripe, adult example：Although the fruit looks ripe, it needs more time to mature before we can eat it. imminent - adj. paraphrase：about to happen very soon synonym：approaching, nearing example：The storm clouds suggest rain is imminent, so we should hurry home unless we want to get wet. convention - n. paraphrase：a formal meeting or accepted way of doing things synonym：conference,...