PassMyExam Study App
9 sessions · ~108 minutes total · Listen in order for best results
This session introduces the fundamental concept of a limit, which is the value that a function approaches as the input approaches some value. We will explore how to estimate limits from graphs and tables, and how to determine limits using algebraic properties. We will also define continuity and its importance in the study of functions, and learn to identify and classify discontinuities.
In this session, we will define the derivative of a function as the instantaneous rate of change and the slope of the tangent line. We will learn how to find derivatives using the limit definition, and explore the relationship between differentiability and continuity. We will also cover the basic rules of differentiation, including the power rule, product rule, and quotient rule.
This session dives into more complex differentiation techniques. We will master the chain rule for differentiating composite functions, and learn how to use implicit differentiation to find the derivative of a relation. We will also explore how to find derivatives of inverse functions, including inverse trigonometric functions.
In this session, we will explore the many applications of differentiation in solving real-world problems. We will learn how to model and solve problems involving rates of change and related rates. We will also introduce L'Hopital's Rule for evaluating limits of indeterminate forms.
This session introduces the definite integral as the limit of Riemann sums, representing the accumulation of a quantity over an interval. We will learn how to approximate definite integrals using various methods, including left, right, and midpoint Riemann sums, as well as the trapezoidal rule. We will also explore the properties of definite integrals.
This session covers the cornerstone of calculus: the Fundamental Theorem of Calculus. We will explore both parts of the theorem, understanding how it connects differentiation and integration. We will learn how to use the theorem to evaluate definite integrals and to find the derivative of an integral.
In this session, we will be introduced to the world of differential equations, which are equations that involve an unknown function and its derivatives. We will learn how to model real-world phenomena using differential equations, and how to visualize solutions using slope fields. We will also learn the technique of separation of variables to solve simple differential equations.
This session focuses on the applications of integration to find the area between curves and the volume of solids with known cross-sections. We will also explore other applications of integration, such as finding the average value of a function and solving problems involving position, velocity, and acceleration. This will solidify your understanding of how integration is used to solve a variety of problems.
In our final session, we will review the key concepts and techniques from the entire course. We will discuss effective strategies for tackling both the multiple-choice and free-response sections of the AP Calculus AB exam. This session will provide you with the confidence and tools you need to succeed on exam day.
AP Calculus AB
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