E-CodeTaylor polynomial: approximation and error — a TI-84 Plus CE program
TAYLOR is a TI-BASIC program for the TI-84 Plus CE. Taylor polynomial of e^x, sin x or cos x about any center, or of ln(1+x) and 1/(1-x) about 0, of any order up to 30: the approximation at x, the true value, the actual error, and the Lagrange error bound where it applies.
What it asks for and what it shows
It asks for 3 values at its prompts, after you pick option 1 from its menu. In the example below it shows PN, F(X), ERROR, BOUND.
Example run
One of its oracle test cases: “e^1 from a 5th-order Maclaurin”. The inputs are typed in order, and the results are the values the case expects on the screen.
| Step | Value |
|---|---|
| You enter | |
| Menu | option 1 |
| Input 1 | 0 |
| Input 2 | 1 |
| Input 3 | 5 |
| The screen shows | |
PN= | 2.716666667 |
F(X)= | 2.718281828 |
ERROR= | 0.001615161792 |
BOUND= | 0.003775391428 |
How it's checked
8 test cases, each checked against an independent method. Replayed key by key on a virtual TI-84 Plus CE, they make 40 checks.
How E-Code checks every program
Run it or put it on your calculator
- Open the library in the TI-84 Plus CE calculator and pick “Taylor polynomial: approximation and error” (TAYLOR).
- Put it on your own calculator with a computer and a USB cable, or type it in by hand.
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All TI-84 Plus CE math programs · All TI-84 Plus CE programs