In this unit, you’ll learn about the essential basics of calculus. Limits and continuity are the backgrounds for all of AP Calculus so it's crucial to understand these concepts. This unit should be about 10-12% of the AP Calculus AB Exam or 4-7% of the AP Calculus BC Exam.
This list will be a good place to start in terms of self-assessing what you need to study or learn. As you are looking through this list write down what topics you don’t remember or still need to learn. Once you identify topics that you would like more help on you can go to the full study guide page for that subunit and get some more information! 📚
Definition of a limit is important to understand as this definition will help us understand derivatives in a later unit.
To read limit notation, you want to start by looking at the a value along the x-axis of the function f(x). Once you reach the a value, you want to evaluate the limit by finding the y value of the function.
This theorem can also be called the sandwich or pinching theorem. The squeeze theorem is used to solve the limit of a function by comparing it to two other functions whose limits are known or easier to compute.
Vertical and Horizontal & Connecting Asymptotes to Limits
Vertical asymptotes can be found when the denominator of the rational expression is equal to zero.
Horizontal asymptotes can be found by looking at the degree of the rational expression. If the degree in the numerator and denominator is the same the horizontal asymptote is the coefficient. If the degree is larger in the numerator the rational expression has a slant asymptote. If the degree in the denominator is larger the horizontal asymptote will be 0.