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