# final taylor polynomial?

does anyone know how to get the final taylor polynomial on a TI89 calculator or a program that can get the final taylor answer?

Relevance

The TI-89 has a Taylor polynomial function built in. If you go under F3 (calc), and scroll down, option 9 is "taylor("

Hitting enter will cause

taylor(

to appear in the command line. Type in the function first, then the variable name, then an integer for the order desired, then the center. So it takes in 4 inputs---note that if you leave off the last input, the calculator will take the center to be zero. For example

taylor(e^(x),x,5)

produces

x^5/120 + x^4/24 + x^3/6 +x^2/2 + x + 1

taylor(e^(x),x,5,1)

produces

e(x-1)^5/120 + e(x-1)^4/24 + e(x-1)^3/6 +e(x-1)^2/2 + e(x-1) + e

It always writes these in descending order (who knows why.)

If you have a complicated function, you can enter it into the graphing assignment screen as y1(x) (or another y), and then enter it into taylor from the home screen. For example, you can go into the graphing assignment page and enter

y1(x) = x^2e^(3x)tan(2x)

And then from the home screen enter

taylor(y1(x),x,6,2)

to get the 6th order Taylor polynomial of that function centered at 2. Note that the third entry must be a positive integer.

• Taylor Series Ti-89