Taylor Polynomials

Press MENU 9 to access the CAS screen.

To obtain the nth degree Taylor polynomial for a given function expanded about x = a, use the syntax

taylor(function, variable, degree, a)

If a is missing, the expansion is taken about a = 0; i.e., a Maclaurin series is displayed.

Press F2 to access the CALC menu. Either press 6 to select 6:taylor, or highlight 6:taylor and press EXE. For example, let's find the fourth degree Taylor polynomial approximation for f(x) = ex about x = 0. After the prompt taylor( in the entry line, type

SHIFT ex ( X ) , X , 4 ) EXE

The screen displays the fourth degree Taylor polynomial for ex.

To find the fourth degree Taylor polynomial approximation for f(x) = ex about x = 2, press F2 to access the CALC menu. Press 6 to select 6:taylor. After the prompt taylor( in the entry line, type

SHIFT ex ( X ) , X , 4 , 2 ) EXE

The screen displays the fourth degree Taylor polynomial for ex expanded about a = 2.