Limits are just Really, Really, Tiny Flashlights #SoME4

An intuitive explanation of limits in calculus — using flashlights. This is my submission for the Summer of Math Exposition 4 (SoME4): an attempt to "elucidate" the concept of limits in a way that gives student a solid visual intuition. Topics covered: - What a limit is and how it relates to finding the value of a function - Holes and jump discontinuities — when the function breaks but the limit still exists - Infinite oscillation and why some limits don’t exist (or still do even with infinite oscillation!) - How derivatives depend on limits to define instantaneous slope - Left-hand and right-hand limits - Limits at infinity and how functions behave far away - The epsilon–delta definition (aka the flashlight–target definition) Who it's for: - High school and college calculus students - Math teachers explaining limits visually - Anyone preparing for AP Calculus, university calculus, or math contests - Viewers interested in SoME4, math visualization, or math education videos Explore It Yourself: Try this Desmos graph to explore the flashlight analogy yourself! https://www.patreon.com/posts/desmos-graph-for-137755159 Special Thanks: Thanks to openclipart.org for the CC0 clipart used in this video — especially the flashlight! Keywords: limits in calculus, understanding limits, limit of a function, calculus explained, calculus for beginners, what is a limit, intuitive calculus, epsilon delta definition, calculus visualization, derivatives and limits, limits continuity, math explained visually, SoME4 math exposition #Calculus #MathExplained #Limits #SoME4 #MathEducation #Derivatives #Desmos