HP 48G - Page 24

Isolating a Variable*
Example: To solve sin x=0: Press(>)SYMBOLIC), then
select =1 at & war... Enterthe expression into
EXPE: (" JSINJa]X)(ENTER). InV¥ak:, specify the variable to
beisolated: (o] &)(X)ENTER). Then, with _PRIMCIPAL un-
checked—to get the general solution—press I
Result : '®=1868#n1"' (or'®¥=w#nl). Thenl isapar-
ameter representing an arbitrary integer; any integer
multiple of 180° (r radians) is a solution.
Computing Taylor Polynomials
Example: Find the 5th-degree Taylor polynomial of
sin x about x = 0. Press (&[RAD)(>)SYMBOLIC), then
select Taglor FPolyd... Enterthe expressioninto
EXPE: (' [SN[a]X)[ENTER); in ¥AF:, specify the variable to
be isolated: (a)(X)[ENTER). Inthe ORDEE: field, enter (5).
Be sure that the KESLLT: field says Sumbiol 1C and
press IITAM. Result: '#-1-31#5"3+1-51%475"
(Press(¥)to see it more clearly in the EquationWriter.)
The Tadlor Pold., tool can calculate expan-
sions only about x = 0, but you can also use it for cal-
culations about x = a by using variable substitution:
You re-express your function in terms of another vari-
able—say, ll—where x=w +a. Then calculate the ex-
pansion and re-substitute (w=x-a). For simpler func-
tions, you can do the initial substitution by inspection;
for more involved expressions, it's easier to let the
machine help you: Just store the substitution 'l+a'
(you choose the numerical value of a here) into the
variable 1. Be sure that the variable Il does not exist
in the current directory path.
Example: Find a 4th-degree Taylor expansion of In x
about x = 1. By inspection, you can replace In x with
In(w+1). Now find its expansion around w=0: Press
(=)symBoLic)and select Tadul o Polud... Nowput
"LHCL+12" in the EXPE: field, M in ¥ak: and 4 in
okpEk:, and press A (Result: 'bl-.5#p*E+7
A1 #h~3-6-41 "4 ) Now make the re-substitution:
XI=J1JENTER) (1) W]STO) the expansion.
(And now you may want to use the rationalizing tool,
{1, to simplify the decimals into fractions—press (<)
(symeoLic) NxT) IEIM). Again, (v) shows the result
more clearly (use (») and (< to scroll as necessary).
*I=olat e war.., works only when the desired variable appears just
oncein the expression (any level of order); So 1we quad.., works for
a variable with multiple occurrences but no higher than second order.
22 THE HP 48G/GX Pocker GUIDE