Module 02 · Lessons 03–07
A limit is a destination, not necessarily a value.
Move toward a point from both sides. Watch the nearby behavior settle before notation gives the idea a name.
Five connected ahas
Nearby behavior, one move at a time.
Each lesson takes about five minutes: move the visual, name what changed, then answer one focused question.
03
What a limit actually meansApproach from the left and right; watch both outputs settle on the same destination.
Start →04Removable discontinuity: a hole can still have a limitSeparate the missing point from the nearby pattern that continues through it.
Move →05Limits at infinity and horizontal asymptotesMove x right and watch a rational function close in on y=3.
Move →06Small angle approximation: why sin(x)/x approaches 1Zoom toward zero in radians and see the ratio settle instead of memorizing the result.
See →07Squeeze Theorem visualizedShrink a neighborhood and watch two parabolic bounds force an oscillating function toward zero.
Squeeze →You will leave able to
- distinguish a limit from the function value at the point;
- read two-sided approach behavior from a graph;
- explain why an undefined expression can still have a finite limit;
- read a horizontal asymptote as a long-run destination;
- explain how two agreeing bounds can force the limit of a trapped function.