Texas Instruments Titanium TI-89, Руководство пользователя

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794 Appendix A: Functions and Instructions
expand(
expression1,var
)
returns
expression
expanded with respect to
var
. Similar powers of
var
are collected. The terms and their factors are sorted
with
var
as the main variable. There might be some
incidental factoring or expansion of the collected
coefficients. Compared to omitting
var , this often
saves time, memory, and screen space, while
making the expression more comprehensible.
expand((x+y+1)^2,y) ¸
y ñ + 2 ø y ø (x + 1) + (x + 1) ñ
expand((x+y+1)^2,x)
¸
x ñ + 2 ø x ø (y + 1) + (y + 1) ñ
expand((x^2
ì
x+y^2
ì
y)/(x^2
ù
y^2
ì
x^2
ù
y
ì
x
ù
y^2+x
ù
y),y)
¸
expand(ans(1),x)
¸
Even when there is only one variable, using
var
might make the denominator factorization used for
partial fraction expansion more complete.
Hint: For rational expressions,
propFrac()
is a
faster but less extreme alternative to
expand()
.
Note: See also
comDenom()
for an expanded
numerator over an expanded denominator.
expand((x^3+x^2
ì
2)/(x^2
ì
2))
¸
2
ø
x
x ñ ì 2
+ x+1
expand(ans(1),x) ¸
1
x
ì ‡
2
+
1
x+
‡
2
+ x+1
expand(
expression1,[var]
)
also distributes logarithms
and fractional powers regardless of
var
. For
increased distribution of logarithms and fractional
powers, inequality constraints might be necessary to
guarantee that some factors are nonnegative.
expand( expression1, [var] )
also distributes absolute
values,
sign()
, and exponentials, regardless of
var
.
Note: See also
tExpand()
for trigonometric angle-
sum and multiple-angle expansion.
ln(2x ù y)+ ‡ (2x ù y) ¸
ln(2
ø
x
ø
y) +
‡
(2
ø
x
ø
y)
expand(ans(1)) ¸
ln(x ø y) + ‡ 2 ø ‡ ( x ø y) + ln(2)
expand(ans(1))|y>=0
¸
ln(x) + ‡ 2 ø ‡ x ø ‡ y + ln(y) + ln(2)
sign(x
ù
y)+abs(x
ù
y)+ e ^(2x+y)
¸
e
2
ø
x+y
+ sign(x
ø
y) + |x
ø
y|
expand(ans(1)) ¸
sign(x) ø sign(y) + |x| ø |y|+ ( e
x
) 2 ø e
y
expr()
MATH/String menu
expr(
string
)
⇒
expression
Returns the character string contained in
string
as
an expression and immediately executes it.
expr("1+2+x^2+x")
¸
x
ñ
+ x + 3
expr("expand((1+x)^2)") ¸
x ñ + 2 ø x + 1
"Define cube(x)=x^3"
!
funcstr
¸
"Define cube(x)=x^3"
expr(funcstr) ¸ Done
cube(2)
¸
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