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  3. ZuAI AP College Board Maths 2020
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Continuity

Next Topic - Non-removable Discontinuities
Study Guide Overview

This guide covers removable discontinuities, focusing on their definition, identification, and removal. It explains how to determine if a discontinuity is removable by evaluating limits. The guide provides worked examples, practice questions, and exam strategies for handling these types of problems. Key terms include continuous function, limit, and removable discontinuity.

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Previous Topic - ContinuityNext Topic - Non-removable Discontinuities

Question 1 of 8

A function fff is continuous at x=cx=cx=c if which of the following conditions are met? 🤔

f(c)f(c)f(c) exists, lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) exists, and lim⁡x→cf(x)=f(c)\lim_{x \to c} f(x) = f(c)limx→c​f(x)=f(c)

f(c)f(c)f(c) does not exist, lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) exists, and lim⁡x→cf(x)≠f(c)\lim_{x \to c} f(x) \neq f(c)limx→c​f(x)=f(c)

lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) exists, but f(c)f(c)f(c) does not exist

f(c)f(c)f(c) exists, but lim⁡x→cf(x)\lim_{x \to c} f(x)limx→c​f(x) does not exist