Limits are just Really, Really, Tiny Flashlights

Описание: 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!
  / 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