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Limits animations

6 verified, narrated animations about limits, reviewed by hand and checked at animation steps. Watch free; download the video or adapt it to your lesson with any paid plan.

Where e comes from: compounding more and more often
Where e comes from: compounding more and more often

This animation tracks one dollar growing under 100% annual interest as the number of compounding periods incre…

Why the area of a circle is pi r^2
Why the area of a circle is pi r^2

A circle is sliced into 16 equal sectors, then unfolded and reassembled into a shape resembling a rectangle wi…

The harmonic series diverges
The harmonic series diverges

Bars representing 1/n shrink toward zero, illustrating why it seems the sum should settle down. The animation …

The squeeze theorem: why sin x / x tends to 1
The squeeze theorem: why sin x / x tends to 1

This animation visualizes why sin x / x approaches 1 as x approaches 0, even though the function itself is und…

The derivative as the limit of secant slopes
The derivative as the limit of secant slopes

An animation tracks secant lines through the fixed point (2, f(2)) on f(x) = x^2/4 + 1/2 as the second point s…

Riemann sums become the integral
Riemann sums become the integral

This animation approximates the area under y = x^2 from 0 to 2 using rectangles, starting with four and doubli…

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