AP Calculus BC Flashcards: Defining Continuity At A Point

Study Defining Continuity At A Point in AP Calculus BC with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

QUESTION

Which type of discontinuity occurs when $\lim_{x \to a} f(x) \neq f(a)$ ?

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ANSWER

Removable discontinuity. The discontinuity can be 'removed' by redefining the function value.

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AP Calculus BC: Limits and Continuity

Algebraic Properties of Limits42 cards

Confirming Continuity over an Interval32 cards

Connecting Infinite Limits and Vertical Asymptotes35 cards

Connecting Multiple Representations of Limits45 cards

You are hereDefining Continuity at a Point38 cards

Defining Limits and Using Limit Notation40 cards

Determining Limits Using Algebraic Manipulation39 cards

Determining Limits Using the Squeeze Theorem34 cards

Estimating Limit Values from Graphs33 cards

Estimating Limit Values from Tables32 cards

Exploring Types of Discontinuities37 cards

All flashcards

38 cards

What this deck covers

This deck focuses on Defining Continuity At A Point, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus BC.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Practice questions

1 of 45Practice questions for this set

Let

s(x)=\begin{cases}\dfrac{x^2-9}{x-3},&x\ne3\\6,&x=3\end{cases}

. Is

s

continuous at

x=3

, and why?

Choose an answer

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