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AP微积分词汇(下篇)

logarithmic function 对数函数

The inverse function to exponentiation.

lower limit 下限

In the definite integral of the form:

a is called the upper limit of the integration.

logistic growth 逻辑增长

If a quantity y increases (or decreases) at a rate that is proportional to both the present amount and the difference between a certain value and its present amount at any time, then we can have a differential equation to solve these problems which are called logistic growth.

Maclaurin polynomial 麦克劳林多项式

The first few terms of the Maclaurin series of a function is called a Taylor polynomial, the order of a Maclaurin polynomial is the order of the highest derivative, which is the last term of the polynomial.

Mean Value Theorem 中值定理

If f is a continuous function on the closed interval [a,b], and differentiable on the open interval (a,b), then there exists a point c in (a,b) such that f"(c)(b-a)=f(b)-f(a).

Maclaurin series 麦克劳林级数

A special series to expand a function f about x=0, which has the form :

midpoint Riemann sum

中点法黎曼和

Approximating the function by its value at the midpoint of the subinterval as the height of the rectangle, and the length of the subintervals as the width of the rectangle to find the area.

nonexistent 不存在

Does not exist

normal 垂直的

Perpendicular, two lines which meet at a right angle.

normal line 法线

A line that is perpendicular to the tangent line

nth term test n 项排除法

If the limit of an is not zero as n approaches infinity, then the series diverges.

numerator 分子

The dividend, the number above the fraction bar

one-sided limits 单边极限

The left-hand limit or the right-hand limit of a function.

parametric equation 参数方程

A group of quantities as functions of one or more independent variables called parameters.

perpendicular 垂直的

Two lines which meet at a right angle.

partial sum 部分和

point of inflection 拐点

A point on a continuously differentiable plane curve at which the curve crosses its tangent, or changes from being concave downward to concave upward or vice versa.

polar coordinates 极坐标

A two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

polynomial function 多项式函数

A function that is defined by a polynomial: consisting of variables and coefficients that involves only the operation of addition, subtractions, multiplication, and non-negative integer exponents of variables.

product 积

The number or expression resulting from the multiplication together of two or more numbers or expressions.

power series 幂级数

The power series in x is an expression of the form:

quotient 商

The number resulting from the division of one number by another.

radius of convergence 收敛半径

If power series converges when |x|r(or |x-a|>r),then r is called the radius of convergence.

ratio 公比

The quotient of in a geometric series.

ratio test 比值法

Let the limit of as n approaches infinity equals L. then the series converges if L<1 and diverges if L>1

rational function 有理函数

A function which can be defined by a rational fraction, an algebraic fraction such that both the numerator and the denominator are polynomials.

related rates 相关变化率

Finding a rate at which one quantity is changing by relating it to other quantities whose rates of change are known.

remainder 余数

The amount left over after performing some computation

removable discontinuity 可去间断点

A discontinuity where the limit of the function at this point does not equal to the value of the function.

restricted growth 受限制的增长

If a quantity y increases (or decreases) at a rate that is proportional to the difference between a certain value and its present amount at any time, then we can have a differential equation to solve these problems which are called restricted growth.

Riemann sum 黎曼和 An approximation of an integral by a finite sum.

right hand limit 右极限

As x approaches c through values greater than c, if the value of the function approaches L, then the left-hand limit of the function at c is L.

right Riemann sum 右矩阵黎曼和

Approximating the function by its value at the right-end point as the height of the rectangle, and the length of the subintervals as the width of the rectangle to find the area.

second derivative 二阶导数

The derivative of the derivative of a function.

separation of variables 变量分离法

One way to solve ordinary and partial differential equations by rewriting an equation so that each of two variables occurs on a different side of the equation.

sequence 数列

A list of numbers written in a specific order.

series 数列

Series are similar to sequences, except they add terms instead of listing them as separate elements. A series has the following form:

sine 正弦

A trigonometric function of an angle, defined as the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle.　　

slope 斜率 A number that describes both the direction and the steepness of a line.

slope field 斜率场

A graph that gives the slope of the tangent to the graph of the differential equation"s solution at each point (x,y) as a function of the point coordinates.

speed 速率

The magnitude of the velocity.

squeeze theorem 夹逼定理

If f(x)≦g(x)≦h(x) and if the limit of f(x) at x=c equals the limit of h(x) at x=c, which is L. then the limit of g(x) at x=c is also L.

subinterval 子区间

An interval that is a subdivision or a subset of an interval.

substitution 换元

One way to solve the antiderivative of a function by substitute the parameter by another form. ( usually to replace the complicated part to make the form easier )

subtraction 减

The operation of deducting one number from another.

sum 和

The result of adding numbers.

Taylor polynomial 泰勒多项式

The first few terms of the Taylor series of a function is called a Taylor polynomial, the order of a Taylor polynomial is the order of the highest derivative, which is the last term of the polynomial.

Taylor series 泰勒级数

A series to expand a function f about x=a, which has the form:

term 项 The elements in the infinite series are called terms

trapezoidal Riemann sum 梯形法黎曼和

The values of the function f on an interval are approximated by the average of the values at the left and right endpoints.

triangle 三角形

A polygon with three edges and three vertices.

trigonometric function 三角函数

A function of an angle, which relate the angles of a triangle to the lengths of its sides.

unbounded 无界

If there does not exist a real number M such that |f(x)|≦M, then the function is not bounded.

upper limit 上限

The definite integral of the form:

b is called the upper limit of the integration.

velocity 速度

A vector which is the rate of change of its position with respect to a frame reference

vertical asymptote 竖直渐近线

The line x=a is a vertical asymptote of the graph y=f(x) if one or more of the following holds: the left-hand limit or the right-hand limit of f(x) at x=a is infinity(positive or negative)　　

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