1·If you want strict equalities in approximations means that we replace the function by its tangent approximation.
如果你想要严格的近似等式,那就意味着我们要用切线逼近来取代原函数。
2·It has a hat because it's a unit vector, and t because it's tangent.
这上面有一个帽子表示它是单位矢量，T表示它是切线。
3·A tangent is a straight line that just touches a curve, so the concept of "running the tangents" is to run the shortest distance possible by running straight from one curve to the next.
切线是一条直线，刚好接触到曲线，所以跑切线是从一个弯道跑到另一个最短的距离。
4·Another way to say it, and I think that is probably closer to the truth, is that these things are somehow placeholders to put values and get a tangent approximation.
换种我认为更贴近事实的说法，它们是通过赋值而得到切线的近似值的，一种占位符。
5·If the two level curves are tangent to each other that means they have the same tangent line. That means that the normal vectors should be parallel. Let me maybe draw a picture here.
如果两个等高线相切，说明它们的切线相同，也就是说他们的法向量应该平行，我再在这里画个图。
1·You could easily argue that a majority of products are primarily tools of purpose, and thus Tangent is their true form language.
你可以很容易地争辩说，大部分的产品的首要目的就是完成作为工具的使命，所以正切就是真正属于它们的造型语言。
2·Of a dielectric the product of dielectric constant and the tangent of its dielectric loss Angle; a measure of the heating effect which occurs in dielectrics.
对于电介质来说，它是介电常数和介质损耗角的正切的乘积，这是对出现在电介质中的热效应的量度。
3·Another reason why hyperbolic tangent is a good choice is that it's easy to obtain its derivative.
另一个原因双曲正切是一个很好的选择是很容易得到它的导数。
4·Note that this code calculates the tangent each time - this is only for clarity.
注意：这代码每次只计算正切—这只是为了清晰。
5·The advanced instrumented impact test equipment and the method for treating test data with the hyperbolic tangent function ensure the accuracy of results.
采用了仪表化冲击试验设备和双曲正切函数回归计算的数据处理方法，因而确保了实验结果的准确性。
1·If the two level curves are tangent to each other that means they have the same tangent line. That means that the normal vectors should be parallel. Let me maybe draw a picture here.
如果两个等高线相切，说明它们的切线相同，也就是说他们的法向量应该平行，我再在这里画个图。
2·And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.
例如，在某些情况下，如果已知向量场与曲线相切，或者内积是一个常数等等，那么结果将会很简单。
3·So, the velocity vector is going to be always tangent to the curve.
速度向量总是与曲线相切的。
4·The other way to think about it, the direction in which the value doesn't change is a direction that's tangent to the level surface.
另一种方法是，函数值不变的方向是,是与等值面相切的方向。
5·They are just flowing along the circle around and around so the flux will be zero. F now is tangent to c.
只是沿着曲线流动，所以通量为零，F与C相切。