HP 39gs

TAYLOR(<expression>,<var_name>,<num>)
Briefly, a Taylor polynomial allows you to approximate a complicated function via a simpler polynomial
function. The <expression> supplied is approximated with respect to <var_name> by terms of a polynomial up
to <num> power.
The screen shot on the right shows the calculator deriving the Taylor
polynomial for sin(x) up to the 7
th
power. The SIN(X) function can be
approximated by taking terms from the polynomial:
3 5 7
x x x
sin( x) =− + − + .... x
3! 5! 7!
1
7
=−
1
x
3
+
1
x
5
− x +....x
6 120 5040
In this example, the result is shown twice. The first is calculated with
MODES set to Standard, the second
highlighting it and pressing
with
MODES set to .
.
Fraction 4 The second screen shot shows the fractional polynomial in more detail after
185