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The basic idea is, you take a guess and you -- whoops -- and you find the tangent of that guess.
首先取个猜想数,然后，嗯,去取猜想数那儿的切线。
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Show me a place where that's not true where the tangent line will be really bad.
请给我个这个原则不对的例子,也就是说切线没起到相应作用的例子。
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That limit will be some arrow we can call the velocity at the time and it will always be tangent to the curve.
那个极限也就是一个矢量,我们称之为瞬时速度,并且它总是和轨迹相切的
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That means that you want to pick, ultimately, a point on this-- this line is tangent to the efficient portfolio frontier with all the other assets in it.
那意味着你会最终会在这上面选一个点-,这条直线是与有效边界相切的,后者包含了所有的资产组合。
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So the velocity at any part of the curve is tangent to the curve at that point.
曲线上任意一点的速度,都在该点和曲线相切
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The tangent's pointing towards the direction you are headed at that instant.
切线的方向就是,速度矢量在那个瞬时的指向
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Tangent means that it has the same slope, it just touches the efficient portfolio frontier for risky assets at one point, and the slope of the efficient portfolio frontier, including the riskless asset, is a straight line that goes through the tangency point, here.
相切意味着斜率相同，它与包含风险资产的有效边界,交与一点，而包含无风险资产的，有效边界，则是一条过切点的直线，切点在这里。
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I don't know how well you can see it in this figure here, is the slope of a straight line connecting these two points, and as the points come closer and closer, the straight line would become tangent to the curve.
我不清楚你们对于这个图像的理解,这条连接两点的斜线,随着两点距离逐渐缩小,两点连线会变成曲线的切线
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At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.
在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度
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Yeah. Suppose I choose it right down there I guess 0. Well, the tangent there will not even have an x intercept. So I'm really going to be dead in the water.
好，如果我选猜想数为0，好吧,这个点的切线甚至和x轴都没交点,所以在这儿这一原则,真的不起作用了。
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