# 微积分网课代修|AP微积分代写AP calculus辅导|MT600A/MT600B TOPICS THAT MAY BE TESTED ON THE CALCULUS AB EXAM

• 单变量微积分
• 多变量微积分
• 傅里叶级数
• 黎曼积分
• ODE
• 微分学

## 微积分网课代修|AP微积分代写AP calculus辅导|TOPICS THAT MAY BE TESTED ON THE CALCULUS AB EXAM

1. Functions and Graphs
Rational, trigonometric, inverse trigonometric, exponential, and logarithmic functions.
2. Limits and Continuity
Intuitive definitions; one-sided limits; functions becoming infinite; asymptotes and graphs; limit of a quotient; $\lim _{\theta \rightarrow 0} \frac{\sin \theta}{\theta} ;$ estimating limits using tables or graphs.

Definition of continuity; kinds of discontinuities; theorems about continuous functions; Extreme Value and Intermediate Value Theorems.

1. Differentiation
Definition of derivative as the limit of a difference quotient and as instantaneous rate of change; derivatives of power, exponential, logarithmic, trig and inverse trig functions; product, quotient, and chain rules; differentiability and continuity; estimating a derivative numerically and graphically; implicit differentiation; derivative of the inverse of a function; the Mean Value Theorem; recognizing a given limit as a derivative.
2. Applications of Derivatives
Rates of change: slope; critical points; average velocity; tangents and normals; increasing and decreasing functions; using the first and second derivatives for the following: local (relative) max or min, inflection points, curve sketching, global (absolute) max or min and optimization problems; relating a function and its derivatives graphically; motion along a line; local linearization and its use in approximating a function; related rates; differential equations and slope fields.
3. The Definite Integral
Definite integral as the limit of a Riemann sum; area; definition of definite integral; properties of the definite integral; Riemann sums using rectangles or sums using trapezoids; comparing approximating sums; average value of a function; Fundamental Theorem of Calculus; graphing a function from its derivative; estimating definite integrals from tables and graphs; accumulated change as integral of rate of change.
4. Integration
Antiderivatives and basic formulas; antiderivatives by substitution; applications of antiderivatives; differential equations; motion problems.
5. Applications of Integration to Geometry
Area of a region, including between two curves; volume of a solid of known cross section, including a solid of revolution.
6. Further Applications of Integration and Riemann Sums
Velocity and distance problems involving motion along a line; other applications involving the use of integrals of rates as net change or the use of integrals as accumulation functions; average value of a function over an interval.
7. Differential Equations
Basic definitions; geometric interpretations using slope fields; solving first-order separable differential equations analytically; exponential growth and decay.

## 微积分网课代修|AP微积分代写AP calculus辅导|TOPICS THAT MAY BE TESTED ON THE CALCULUS BC EXAM

Any of the topics listed above for the Calculus $\mathrm{AB}$ exam may be tested on the $\mathrm{BC}$ exam. The following additional topics are restricted to the $\mathrm{BC}$ exam.

Functions and Graphs
Parametrically defined functions; polar functions; vector functions.Limits and Continuity

Differentiation

Derivatives of polar, vector, and parametrically defined functions; indeterminate forms; L’Hôpital’s rule.

Applications of Derivatives

Tangents to parametrically defined curves; slopes of polar curves; analysis of curves defined parametrically or in polar or vector form.

The Definite Integral

Integrals involving parametrically defined functions.

Integration

By parts; by partial fractions (involving nonrepeating linear factors only); improper integrals.

Applications of Integration to Geometry

Area of a region bounded by parametrically defined or polar curves; arc length.

Further Applications of Integration and Riemann Sums

Velocity and distance problems involving motion along a planar curve; velocity and acceleration vectors.

Differential Equations

Euler’s method; applications of differential equations, including logistic growth.

Sequences and Series

Definition of series as a sequence of partial sums and of its convergence as the limit of that sequence; harmonic, geometric, and p-series; integral, ratio, and comparison tests for convergence; alternating series and error bound; power series, including interval and radius of convergence; Taylor polynomials and graphs; finding a power series for a function; MacLaurin and Taylor series; Lagrange error bound for Taylor polynomials; computations using series.

## 微积分网课代修|AP微积分代写AP calculus辅导|TOPICS THAT MAY BE TESTED ON THE CALCULUS AB EXAM

1. 函数和图形
有理函数、三角函数、反三角函数、指数函数和对数函数。
2. 限制和连续性
直观的定义；片面限制；函数变得无限；渐近线和图表；商的限制；林一世→0罪⁡一世一世;使用表格或图表估计限制。

1. 微分
导数的定义是差商的极限和瞬时变化率；幂函数、指数函数、对数函数、三角函数和反三角函数的导数；乘积、商和链式规则；可区分性和连续性；以数字和图形方式估计导数；隐分化; 函数逆的导数；中值定理；将给定的极限识别为导数。
2. 衍生品
的应用 变化率：斜率；临界点；平均速度; 切线和法线；增加和减少功能；对以下问题使用一阶和二阶导数：局部（相对）最大值或最小值、拐点、曲线草图、全局（绝对）最大值或最小值以及优化问题；以图形方式关联函数及其导数；沿直线运动；局部线性化及其在逼近函数中的应用；相关费率；微分方程和斜率场。

3. 积分作为黎曼和的极限的定积分；区域; 定积分的定义；定积分的性质；黎曼使用矩形求和或使用梯形求和；比较近似总和；函数的平均值；微积分基本定理；从其导数绘制函数；从表格和图表中估计定积分；累积变化作为变化率的积分。
4. 积分
反衍生物和基本公式；替代抗衍生物；抗衍生物的应用；微分方程; 运动问题。
5. 将积分应用于
区域的几何区域，包括两条曲线之间；已知横截面的实体的体积，包括旋转实体。
6. 积分和黎曼和的进一步应用
涉及沿线运动的速度和距离问题；其他涉及将利率积分用作净变化或将积分用作累积函数的应用；一个函数在一个区间内的平均值。
7. 微分方程
基本定义；使用坡度场的几何解释；解析求解一阶可分微分方程；指数增长和衰退。