前言：这里只罗列出一些重要的点，一来是知识点的梳理，二来便于查阅。
1.夹逼定理
英文叫做Squeeze theorem。维基百科是这样定义的：
Let I be an interval having the point a as a limit point. Let f, g, and h be functions defined on I, except possibly at a itself. Suppose that for every x in Inot equal to a, we have:
( g(x)leq f(x)leq h(x) )
and also suppose that:
( lim_{x ightarrow a}{g(x)} = lim_{x ightarrow a}{h(x)} = L )
then:
( lim_{x ightarrow a}{f(x)} = L )
- The functions g and f are said to be lower and upper bounds of f.
- Here, a is not required to lie in the interior of I. Indeed, if a is an endpoint of I , then the above limits are left- or right-hand limits.
- A similar statement holds for infinite intervals: for example, if I = (0,infinite),then the conclusion holds, taking the limits as x -> infinite.
如果不纠结于数学的严谨性的话，夹逼定理的意思就是上线和下线都逼近于L，那么作为被夹在中间的f(x)也注定会逼近于L。
2.泰勒展开式
这个还是很有用的，它可以把很多复杂的函数近似成容易处理多项式。可导函数f(x)的泰勒展开式是：
作为一种special case,还有一个麦克劳林展开式
这个是在0点展开式的泰勒展开。
一些常用的泰勒展开式是需要记住的，比如-ln(x)在1的展开式是1-x，这个以后补。
3.导数
一阶导数曲为线的斜率，衡量曲线变化的快慢和方向。二阶导数反应曲线的凹凸性。
下面是常用的导数公式，这个主要靠背。
C'=0
(xn)' = nxn-1
(sin x)' = cos x
(cos x)'=-sinx
(ax)' = axlna
(ex)' = ex
(logax)' = (1/x)logae
(ln x)' = (1/x)
(u+v)' = u'+v'
(uv)' = u'v+uv'