x squared

X^ 2+ 9/ x^ 2 Then you can minimize x squared plus nine over x squared.

然后你就可以最小化。

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The total energy that I started with if I release it here at zero speed equals^ 2 one-half k x max squared.

开始的总能量，如果我在这里释放它，初速为0，总能量，=1/2kx的最大值。

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And I continued the problem correctly, because I wrote down here one-half k x max squared, which is exactly this term.

继续正确解答这个问题，因为我在这里写下，1/2xmax^2，就是这一项。

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That must be, now, 1/ 2mv^ 2 one-half m v squared x at a random position x, which is the potential energy at position x.

那么现在肯定，是等于，位于一个随意位置，这是在x位置的，势能。

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In the case of the spring, was proportional to x squared and out came a perfect simple harmonic oscillation, no approximation necessary.

在弹力的例子里，和x^2成比例，所以得到一个完美的，简单谐波震荡，不是非常重要。

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Do you know how to integrate X squared times E to the minus X, without looking it up?

你知道怎么不查书也能求出x平方乘e到负x的积分？

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Divided by n plus x squared.

除以n加x的平方。

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X^ 2+ y^ 2 But maybe you can observe that this is x squared plus y squared.

但你有可能会观察到这是。

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We don't have that square root of one minus x squared anymore.

这里没有1-x的平方的平方根了。

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Or it's1/ 2 k x squared.

或者是1/2，k，x的平方。

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And then the equation xy equals three becomes, well, x squared equals three. I have two solutions.

然后这个xy=3的式子变成了怎样呢，变成了x^2=3，我现在有两个解。

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