TongZhuo's Blog

Text 2 Parenting tips obtained from hunter-gatherers in Africa may be the key to bringing up more contented children, researchers have suggested. The idea is based on studies of communities such as the Kung of Botswana, where each child is cared for by many adults. Kung children as young as four will help to look after younger ones and “baby-wearing”, in which infants are carried in slings, is considered the norm. According to Dr Nikhil Chaudhary, an evolutionary anthropologist at Cambridge...

Title: Threads of Conspiracy: When Worlds Collide Main Idea: A tech scandal, environmental sabotage, and political corruption intertwine across multiple settings, revealing hidden connections through the lens of ordinary people caught in extraordinary chaos. 【The Glitch in the System】 In a sleek urban tech hub, engineer Mia stared at the console, her fingers flying to evaluate the erratic algorithm. “This isn’t just a glitch,” she muttered, noticing subtle code alterations that corresponded...

type one：根据极限化积分 本质还是和之前的积分一样，传送门 提出来一个1m或者1n\frac{1}{m}或者\frac{1}{n}m1​或者n1​当dx或者dy，in或im变成x或ydx或者dy ，\frac{i}{n}或\frac{i}{m}变成x或ydx或者dy，ni​或mi​变成x或y 哎呀，其实都一样，就是一个变成了两个 跳过 type two：根据奇偶性简化运算 第一道 从-1到1，x的范围对称，所以看被积函数关于x的奇偶性，第一个项是偶函数，所以这一部分翻倍，第二项是奇函数，所以抵消 第二道 积分区域关于x、y轴对称 把被积函数展开，x2，4y2x^2，4y^2x2，4y2偶函数翻倍，4xy4xy4xy光看x是奇函数，所以抵消，就不用看y了，x和y就看一个，哪个起作用看哪个 type three：求带有积分的极限 这种类型不管长的多唬人都有两个东西 一个是等价无穷小替换或者泰勒展开，另一个是洛必达 先把分母无穷小替换了，然后洛必达 对于分母可以变成极坐标下的二重积分，θ可以直接算出来，后边变成了关于ρ的积分，直接根据这个技巧求导 type...

Ano? – What? Sino? – Who? Babae – Woman Lalaki – Man Oo – Yes Hindi – No Ba – (Word used for “yes” and “no” questions) Ko – My Mo – Your Niya – His/Her Nag-aaral – Studying Nagtatrabaho – Working

释义列表 evaluate - v. ◦ paraphrase：judge the value or quality of something ◦ synonym：assess, judge ◦ example：The teacher will evaluate our projects tomorrow, which makes everyone nervous about their grades. console - v. ◦ paraphrase：comfort someone in distress ◦ synonym：comfort, soothe ◦ example：She tried to console her friend after the loss, even though she felt helpless herself. assassinate - v. ◦ paraphrase：murder a prominent person for political reasons ◦ synonym：kill, murder ◦...

二重积分的计算法 直角坐标 以这道题说明方法 先对Y积分，因为Y的范围一下就看出来了，而且对X的范围用y表示的时候也比较方便 ∫−12dy∫y2y+2dx\int_{-1}^{2}dy\int_{y^2}^{y+2}dx∫−12​dy∫y2y+2​dx 也可以换一下积分顺序，但是比较麻烦 有的原函数不能用初等函数表示，所以积分顺序是唯一的，弄错了就积不出来 利用对称性和奇偶性简化计算 积分区域关于x轴对称时，被积函数是关于y的奇函数可以抵消，偶函数翻倍 关于y轴对称时也一样 以a(x,y)=2x2ya(x,y)=2 x^2 ya(x,y)=2x2y的图像进行说明，不想死记公式，公式记多不仅痛苦还容易忘 积分区域关于x轴对称，关于y的奇函数，一半体积向上，一半向下，抵消了 极坐标 对x和y的积分变成了对θ和ρ的积分 判断θ的范围：以x轴的正方向为标准，从0开始，π2\frac{π}{2}2π​到y轴的正方向，−π2-\frac{π}{2}−2π​到y轴的负方向，看转多少范围可以把积分区域包起来，范围就是多少，转一圈才能把积分区域包起来的话，那就是0 ~...

释义列表 comedy - n. paraphrase：funny play or film synonym：humor, farce example：The comedy was so amusing that the audience laughed even when the actors forgot their lines. consumption - n. paraphrase：act of using up resources synonym：use, expenditure example：The government urged people to reduce energy consumption because power plants were overloaded. defeat - v./n. paraphrase：win against someone; failure synonym：beat, overcome example：If we defeat this team, we’ll advance to the...

type one：求极限 还是之前那种套路，和一元函数求极限没什么区别，不贴题了，过 type two：复合函数求偏导 还是链式法则的运用，哎呀，可烦这种套娃题型 第一种是这样，把函数都亮出来了，这个比较明晰，就是算起来可繁琐 第二种是给了一个抽象函数，抽象函数里边有好几个参数，like this 要点就是：先对外边的函数求导，然后对着里边的函数求导 对于第二种类型可以写f1′,f2′f'_1,f'_2f1′​,f2′​ 最最最最套娃的题，就是第二种类型求二阶导，像下边这样 不过有一点好处就是可以抄一阶导的结果：括号里边的式子都是抄一阶导的结果； 还有一点就是： f12′′=f21′′{f}'' _{12}={f}'' _{21}f12′′​=f21′′​ !!!,合并的时候一定要把这两项给合并在一起 type three：给出两个好像没有关系的式子，然后求偏导 最奇怪的就是这道题，用实际例子去理解这道题 假设z=u2+v2z = u^2 + v^2z=u2+v2，其中u=x+yu = x +...

释义列表 cunning - adj./n. paraphrase：clever at deceiving others synonym：sly, crafty example：Although the fox was cunning, it couldn’t escape the trap that the farmer had set near the fence. burst - v./n. paraphrase：break open suddenly or explode synonym：explode, rupture example：The balloon burst when it touched the thorny bush, which startled the children playing nearby. superfluous - adj. paraphrase：more than needed; unnecessary synonym：excess, extra example：The teacher asked us to...

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