## 1. 切线问题

Tangent Line一个不严格的概念：

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point.

## 2. 极限

Suppose f(x) is defined when x is near the number a. (This means x that is defined on some open interval that contains a, except possibly at a itself.) Then we write:

and say “the limit of f(x), as x approaches a, equals L”
if we can make the values of f(x) arbitrarily close to L (as close to L as we like) by
taking x to be sufficiently close to a (on either side of ) but not equal to a.

Roughly speaking, this says that the values of f(x) approach L as x approaches a. In other words, the values of f(x) tend to get closer and closer to the number L as x gets closer and closer to the number a (from either side of ) but x != a.

• 1st Rev. 11/06/19
• 2nd Rev. 11/13/19
1. Calculus, James Stewart, 7ed  2 3 4