Moving the Centre

Expand where it helps most

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Taylor series can be centred at any point a where the function is smooth.
• Centre the series near where you need it: the error grows like |x − a|ⁿ⁺¹.
• Lagrange’s remainder: the error is about the size of the first omitted term.

Steps

1. No series at zero
2. Taylor series anywhere
3. Pick the best centre
4. A logarithm by hand
5. How big is the error?
6. Six decimal places of e