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Who was also one of the word's first programmers. So she was trying to write this program, and it didn't work.
也是世界上最早的几个程序员之一,她正尝试着完成一个,复杂的求反正切的程序。
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And the fourth thing to notice is, I've used abstraction. I've said nothing about how I'm going to make square root.
第四件事情就是，我运用了抽象,我对怎么去求平方根没有提及。
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Please accept my present, which has been brought to you, for God has favored me, and I have plenty.
求你收下我带来给你的礼物，因为神恩待我，使我充足。
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You've got to juggle the two equations, multiply that by 4, multiply that by 3, add and subtract and so on.
同时处理这两个方程,这个两边乘以4,另一个两边乘以3,将两方程相加或相减求出答案
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What he says you should do instead is to take the geometric average of gross returns.
他认为应该,对每年的收益求几何平均
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Detachment, buddy, and only detachment, desirelessness, cessation from all hankering.
超然，巴蒂，唯一的超然，无欲无求，所有的渴望欲望停止。
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We're going to ask for the same grade game we played at the beginning.
我们来求成绩博弈在此情况下的结果
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Now let's take it in the other order.
我们用另一种顺序求二阶偏导数。
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Take the difference of the two velocities and divide by the difference of the two times, and you've got the acceleration.
求出速度的差值,除以时间的差值,这样就能得到加速度
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So I'm hoping you guys are comfortable with the notion of taking one or two or any number of derivatives.
我希望你们,能习惯求一阶,二阶,或者任意阶导数的概念
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In there, I want to make this distinction, this nuance: the evaluator is still going to be taking those expressions and using its rules to get a value, but it's not going to print them back out.
在这里，我想要做这么一个，细微差别：运算器依然会,对表达式,进行求值，但是不会,显示结果值。
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First, it's pointing to the beginning of the list, which initially might be down here at but after a while, might be part way through. And to that, I simply add a halfway point, and then I check.
列表中间的一个部分了，然后我求出列表的中值点,然后看看该点的值是不是等于目标值，如果是的话就完成了，如果不是的话，如果中位值大于我要找的目标值。
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Can you imagine a study of relationships throughout human history ? that focuses on the average?
你能想象,对整个人类历史上的恋爱关系进行研究,并求平均值吗？
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A creature is required who is distinguished in certain ways from other animals.
是一种对之有所求的创造物,他在某些方面与其他动物不同。
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That's another conventional formula that goes from interest rate to price of the security.
这是另一条已知利率,求证券价格的经验公式
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You're not pinned down to a place working for a living.
你不会被阻止去一个地方工作求活。
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And I know it's kind of, you can see it on your handout, it has the rest of the pieces over here.
我可能会去求它们的长度，我知道这有点儿，你们可以在课堂手册上看看。
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In my days, they would say, "Find out when you want an object to go through that point."
我读书的时候,老师要求我,"求出物体何时经过该点"
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It's going to take a little bit more work, so let's see if we can do it.
这看起来有点麻烦，让我们看看怎么求复杂度。
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In the case of a recursive exponentiator, I'm going to do the following trick.
在这个迭代求乘方的例子里面，我会用这么个小把戏。
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Again as I suggested if I've got two integers and I want to find common divisors I could take those two lists and walk through them.
我还要说如果我们有了两个整数,并且想求两者的公因数的话我,可以把这两个整数的。
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This was using something called a bisection method, which is related to something called binary search, which we'll see lots more of later, to find square roots.
你应该想起来,我们是以一个,叫做二分法求平方根的问题结束的，它运用了二分法去求一个数的平方根，二分法和我们将要花很多时间。
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It's useful to have the average acceleration, which you can find by taking similar differences of velocities.
平均加速度也是很有用的,你可以用类似方法,取速度的变化量求出来
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You add them all up algebraically, keeping track of their sign, and that's the total force.
你再对这些力做代数加法,注意符号,就求出合力了
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He greets his former rival and enemy with these words 1 This is in Genesis 33:10-11 If you would do me this favor, accept for me this gift, for to see your face is like seeing the face of God, And you have received me favorably.
他用以下的话来迎接往昔的仇敌,这段话出现在《创世纪》10章第10到11节中1,不然，我若在你眼前蒙恩，就求你从我手里收下这礼物，因为我见了你的面，如同见了神的面，并且你接纳了我。
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Of course, you can take a function and take derivatives any number of times.
当然,你可以随意拿一个函数,对它求任意阶的导数
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If it's not greater than x, take 3. Square it.
那么就跳到2，求它的平方。
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The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.
解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件
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We can start taking derivatives of this with respect to time.
我们首先来对时间求微分
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