🏠 Adventure 11 — Taylor Series
Taylor series as a ‘function builder’: use derivatives to construct ex, sin(x), and cos(x), then connect to Euler’s identity.
🎯 What you will learn
- Velocity is the slope of the height graph.
- Distance fallen is the area under the velocity graph.
- Constant acceleration makes v(t) a straight line and y(t) a curve.
📖 1) Read / Listen: Story
✏️ 2) Do the Adventure Activity
📈 3) Charts
⚡ Optional “Next Idea”
If velocity grows linearly, what happens to v²?
That question leads to an energy preview: 2ax = v² (constant acceleration).