数学巴朗ap微积分 pdf求助 ap

来源：蜘蛛抓取(WebSpider) 时间：2016-04-29 16:40 标签： ap微积分bc真题下载
ap 微积分 f(x)=定积分：根号下(t^2-t)dt.上限：2x;下限:4.求f(2)的导数.
f(x)是变上限积分函数,f'(x)=2根号((2x)²-2x),带入x=2得2根号12
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AP微积分中用到的高中数学知识
来源：新东方网整理
　　微积分中用到的高中知识主要是函数相关知识，主要有以下几方面内容：
　　1. 函数的定义、函数的图像、分段函数、绝对值函数、定义域和值域等;
　　2. 函数的运算及复合函数，函数图像的对称性;
　　3. x的n次幂的函数、反比例函数、多项式函数、有理函数、三角函数的定义、性质和图像分析;
　　4. 反函数和反三角函数的图像和性质;
　　5. 指数函数和对数函数;
　　6. 参数方程(只是Calculus BC所要求的内容)
　　这些基础内容的讲解将主要以做题带动讲解的方式，通过一定数量的例题引导，加速学生对基础知识的回忆，为后面的微积分学习打下一定的坚实基础。
　　1. 函数的基本知识
　　1.1. Definition
　　If a variable y depends on a variable x in such a way that each value of x
determines exactly one value of y, then we say that y is a function of x.
　　1.2. The vertical line test:
　　A curve in the xy-plane is the graph of some function f if and only if no
vertical line intersects the curve more than once.
　　1.3. The absolute value function
　　2. 函数的运算
　　2.1. Composition of f with g
　　Given functions f and g, the composition of f with g, denoted by f ο g, is
the function defined by
　　The donation of f o g is defined to consist of all x in the domain of g for
which g(x) is in the domain of f.
　　2.2. Symmetry Tests
　　a) A plane curve is symmetric about the y-axis if and only if replacing x
by –x in its equation produces an equivalent equation.
　　b) A plane curve is symmetric about the x-axis if and only if replacing y
by –y in its equation produces an equivalent equation.
　　c) A plane curve is symmetric about the origin if and only if replacing x
by –x and y by –y in its equation produces an equivalent equation
　　3. 常见的函数
　　3.1. Inverse function
　　A variable is said to be inversely proportional to a variable x if there is
a positive constant k, called the constant of proportionality, such that,
　　3.2. Polynomials
　　A polynomial in x is a function that is expressible as a sum of finitely
many terms of the form cxn, wherec is a constant and n is a nonnegative
　　3.3. Rational function
　　A function that can be expressed as a ratio of two polynomials is called a
rational function.
　　4. 反函数
　　4.1. Inverse function
　　If the function f and g satisfy the two conditions：
　　g(f(x))=x for every x in the domain of f
　　f(g(x))=y for every y in the domain of g
　　then we say that f is an inverse of g and g is an inverse of f or that f
and g are inverse functions.
　　4.2. The Horizontal Line Test
　　A function has an inverse function if and only if its graph is cut at most
once by any horizontal line.
　　5. 指数函数、对数函数
　　5.1. A function of the form f(x)=bx, where b&0, is called an exponential
function with base b.
　　5.2. The basic characteristic of exponential function
　　5.3. The basic characteristic of logarithmic function
　　5.4. If b&0 and b≠1, then bx and logbx are inverse functions.
　　6. 参数方程
　　6.1. Definition
　　Suppose that a particle moves along a curve C in the xy-plane in such a way
that its x- and y- coordinates, as functions of time, are
　　x=f(t), y=g(t)
　　We call these the parametric equations of motion for the particle and refer
to C as the trajectory of the particle or the graphs of the equations. The
variable t is called the parameter for the equations.
(编辑：张剑乔)
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