Removing Discontinuities
Samuel Baker
7 min read
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Study Guide Overview
This study guide covers removing discontinuities in AP Calculus AB/BC. It focuses on identifying and removing removable discontinuities by factoring, canceling terms, and redefining the function. It also explains how to ensure continuity in piecewise functions by matching limits and function values at boundaries. The guide uses examples and practice problems involving both algebraic and graphical approaches to understanding continuity. Finally, it provides practice questions in multiple-choice and free-response formats.
#AP Calculus AB/BC: Removing Discontinuities - Your Ultimate Guide
Hey there, future AP Calculus master! 👋 Let's tackle discontinuities together, making sure you're super confident for the exam. We'll focus on making those tricky functions smooth and continuous. Let's dive in!
#1.13 Removing Discontinuities
This section is all about understanding and fixing those pesky breaks in graphs. Remember, a continuous function is one you can draw without lifting your pencil!
#⭕ What are Discontinuities?
Discontinuities are points where a function isn't... well, continuous. Think of them as gaps, jumps, or holes in your graph. We've got three main types, but we're focusing on removable discontinuities today.
Image courtesy of LibreTexts Mathematics
#📍 Removable Discontinuities
Removable discontinuities are like "holes" in a graph. The function isn't defined at that point, but the limit exists. We can "fill" this hole to make the graph continuous.
A removable discontinuity occurs when the limit of a function exists at a point, but the function is either undefined or has a different value at that point.
Image courtesy of LibreTexts Mathematics
In this graph, the limit as approaches ...
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